By level 9 bard has 7 level 3 spells. With 6-8 expected encounters you can drop an 8d6 minimum spell every encounter.
So 1st round 8d6 minimum, then two rounds of 2d10+2d6.
The 8d6 part is likely to hit multiple targets and lightning bolt can be easy to avoid hitting your own mooks
You either completely missed the point here or are deliberately ignoring it. I never disputed that and included it in my comparison. The discussion has been based on damage per encounter with the assumption it's maintained through the day by budgeting 1 slot per encounter. The damage per encounter isn't going up or down regardless of the number of encounters because it's based per encounter in the first place.
You are also moving the goal posts by changing from fireball to lightning bolt, likely in response to realizing the point against fireball was correct. It was a pointless move because I was always allowing for the benefit of the doubt and giving the damage for the spell once per combat. The point about not using fireball as often due to friendly fire was just pointing it out, but the damage was still included. I agree lightning bolt would work better and used it in an earlier example with a druid. 8d6 damage doesn't change from 8d6 damage in changing spells.
The point is the bard cannot do as much you are claiming. Right now we're changing from fireball to lightning bolt. We cannot claim to have both because you are using 3 non-bard spells at 9th level: eldritch blast, lightning bolt, hex. We are also going with variant human because that is required to pick up eldritch blast plus 2 more spells at this point. An ASI at 4th and 8th level to cap CHA mean a person cannot claim more feats.
This example has no more spell secrets to work with, doesn't have these ones with any other race, and doesn't have these ones with any other bard subclass. This is important to point out because the premise that bards are overpowered by something a specific race and subclass are using is applying a trait not representative of the class.
Level 10 destructive wave doesn't hit your team mates plus knocks prone.
Yes. It does that. That seems appropriate for a 5th level spell. It does that well within movement speed and that loses the range advantage to do the same damage the lightning bolt in the same slot would do. It also takes another magical secret. These are limited.
They still have another 10-14 known spelks if allies are in the way. And aoe spells don't miss and they don't rely on allies.
Yeah, I already assumed no save bonus when looking at damage, and applied damage on a save when appropriate. I do that because saving throw bonuses tend to be small and rare while armor class does tend to go up.
Only if the bard took one of those spells in the spells known. That's one of the points you are missing or ignoring. When you bumped up from 9th level to 10th level on the lore bard the total number of spells known became 16. You have lightning bolt, hex, and destructive wave.
Rogues often win initiative and can't sneak attack. Or fly critters with no flying allies.
Readying an action solves the initiative issue. That's never been a problem. I agreed range can be an issue earlier but it's not constant and there are many ways to gain advantage for the sneak attack.
Blaster bard damage isn't reliant on allies.
Never said they were, but range gets harder to maintain if there's no one between them and your squishy butt, lol. Especially if you switch to destructive wave and they are now only 30' away for you to be doing damage.
That's in top of bard dice which can be used on skills, song if rest and actual bard spells like invisibility, enhance ability, hypnotic pattern, heat metal etc.
Inspiration dice don't even need to be used on skills. They can be used to any ability check. The problem is repeat rolls empties the pool fast and the dice are usually better spent on inspiration or cutting words. Reliable talent is better than peerless skill and accessible at the levels you were discussing for damage and at 14th level when peerless skill becomes available.
You seem to be presenting Shrodinger's Bard again. A bard cannot cast what he might have taken from the bard list. He can only cast what he has actually taken. That's why I posted actually spell selections at every level.
Here's what happens. You are assuming 2 short rests. You are assuming hex at all times. Hex lasts an hour and short rests take an hour. You had 3 first level slots for hex and it requires a minimum of 3 first level slots to cover hex and that's still assuming not losing it or dropping it for another spell. At 10th level you get 4 first level slot from then to the end of time.
You don't have 1st level slots to spare to recast hex. If you cast invisibility, enhance ability, hypnotic pattern, or heat metal (your examples) you used 1 of your 3 second level slots that you have until the end of time and lost the hex you currently have. You either give up hex or give up another slot to renew it. Hex kills your low level slots with this build. You won't have enough higher level slots to cast those and renew hex and justify a strong damage spell per encounter until 13th or 14th level.
A Rogue has to sneak attack a blaster bard doesn't have to blast.
You don't have to blast but you do if you want to do damage and have it considered part of the analysis.
You seem to be taking hypnotic pattern. So percentage of the time? 50/50 support vs attacking? It's not hard to lower the expected potential damage based on blasting with your bard focused on blasting because he's not actually blasting.

That's why I said the only direction you have to go from what I listed is down. I'll remind you the number of times you cast hypnotic pattern is also the number of times you recast hex. If you want to argue this line I'll expect a lot less hex damage.
Which gets back to you missing or ignoring the points I made. Concentration makes keeping hex up all the time is either unrealistic or locks out those other spells you mentioned.
Rogues don't have to sneak attack either. They get to continue sneak attack while the bard does something else, which skews the damage you are claiming even more towards the rogues. On that same note, fast hands is an example of a useful bonus action while not having to give up sneak attack (it lowers chance to hit with it). Arcane tricksters also have spells and can leverage them for sneak attacks or other useful options. Assassins get a free poisoner kit proficiency for a reason and they can be good at harvesting their own poisons.
Bard dice are also hitting d8s and d10s which is actually better than expertise.
Peerless skill becomes available at 14th level. The lore bard cannot use bardic dice on himself until then. It's not even as good as the help another action for free at lower levels other than it stacks.
The correct comparison would be peerless skill vs reliable talent. The average bonus on this system uses 10, 15, and 20 DC's as the most common checks. With absolutely no ability score bonus at 14th level when peerless skill becomes available a rogue has 0% failure on any 15 check in which he's proficient and 0% failure on any skill with expertise.
For example, a rogue with 10 CHA auto-succeeds any DC 20 NPC favor request with expertise in persuasion starting at 14th level for the 5e version of the diplomancer build. That doesn't allow the impossible, change consequences, or create it's own consequences by harassing one's associates all the time. It's a demonstration of how useful this ability is.
Give the bard a 20 ability score compared to the 10 ability score for the rogue at the same level and a combined roll of 4 or less on the dice still fails that DC 20 check. Give the bard a 10 ability score to match the rogue and a combined roll of 9 or less fails the check. That's comparing a limited resource to an always-on ability.
Granting that bonus to someone else still carries that fail chance, especially since expertise to double the proficiency check is highly unlikely to be a factor. Bards do not out skill-rogues just like they don't out-heal clerics, out-blast nukers, out-fight fighters, or out-tank barbarians.
Reliable talent also comes online close to 10th level when you are adding destructive wave and is arguably the best skill-based ability in the game. You keep on fighting the good fight arguing that one though.

Limited yes but if you really need to pass the average roll is more than expertise and applies to any skill.
No, it applies to any ability check. There is a difference between a skill and an ability check. You can use it on initiative and go first if you want. First strike potential on a lore bard is useful, especially if you want to continue with fireball instead of lightning bolt yourself at higher levels, or just beef up that assassin's odds of going before someone else.
How many checks you need to use it for is more of an issue. See my comments on reliable talent above. It's better. Plus the word "average" is relevant. A static bonus is a guaranteed +4 bonus (depending on level OC) and preferable to the 37.5% chance of a lower roll on a d8, imo.
Plus cutting words as well.
How many dice do you have left after handing out inspiration to the party so they could pretend they have expertise on a single check? Those dice disappear fast. I find the best use is still handing them out for the attack or save bonus. Cutting word for emergency protection or reducing damage is good but less impactful in the long run. Used for skills is more situational. That's how I prioritize those 3-5 dice.
Outside combat jack of all trades and enhance ability are also good.
Enhance ability can usually be done with the help action and conflicts with hex for concentration. These are 2 long term concentration spells so you wouldn't even be recasting hex if you were using enhance ability and definitely down damage while enhance ability is maintained.
Bards always good regardless rogue may not be.
Disagree. Rogues are better at skills because expertise comes sooner and reliable talent is huge. The damage you are showing is behind multiple rounds of sneak attack. Evasion and cunning action are good for survivability and bards tend to be squishy. It takes deliberate construction that creates scenarios to make a rogue not good for something.
Note this is something bards are not good at and it's competitive IMHO. Even if the rogue wins (both classes are situational in a rl game) it's not going to be by that much and damage isn't a bard thing.
That's what makes the bard so good you can build them to be decent at something they're supposed to be bad at.
Replace "supposed to be" with "supposedly". There's no rule or guideline that says bards are not supposed to be good at any particular option. Then replace "good" with "good enough". Adding a damage option here really hasn't gone anywhere special. This is adding a good enough damage option when the class is supposedly not good at damage. It's still not special and simply didn't take other reasonable choices.
And that's just on thing they can do. You could build one to focus on healing instead and it's still useful due to the class abilities and actual bard spell list.
It's useful because the alternative is not useful? So, WAI? Were you expecting that a bard should have spell list full of ribbon abilities and fluff or something, lol? The goal is to be useful. The benefit is giving up being the best at anything and being useful support with options.
Yes, a bard can pick up a few spells and then cast them with equal-to-or-less-than ability compared to other full casters with a customization option (secrets) after another full caster would have already had the spell for 1 or more levels.
The bard still isn't close enough to those casters in their chosen fields to validate that claim. The bard has a useful variety of options.
You could pick spells like banishment or just cherry pick good spells and not focus on anything. Healing spirit plus fly/haste/fireball or whatever is still good.
So a bard cherry-picking a few spells from the wizards list is over-powered because the bard also has good spells, even though the wizard has been cherry-picking the best wizard spells at every single level, got them first, and can cast them better? Replace "wizard" with "cleric" in the preceding paragraph and repeat? That doesn't seem logical.
The bard's breadth cost a lot of focus in respect to either of those classes. The closest competitor to the bard is actually the druid as a cleric / wizard support hybrid and that turns into a debate between the value of wildshape vs inspiration+skills if you want look at that too for an over-all comparison.
