So you don't have
hex and it cannot be part of the damage calc. There's no damage from it to add. Your at-will attacks are doing 2d10 damage for 7.7 DPR. The TWF rogue does 7.5 DPR if he's landing 0 sneak attacks. That's at 6th level, 2 short swords, +4 DEX bonus. Your damage sucks in comparison.
Fireball does 8d6 damage. That's 28 damage on average, or 14 on a save.
TWF gives two chances to land that 3d6 sneak attack damage. That's where the accuracy comes from. It's extremely easy to gain sneak attack. 3 rounds with 3 sneak attacks is 9d6 damage. That's more than your 8d6 fireball by itself but the rogue's base attacks are also included. I'll drop the second weapon attack if the first weapon attack hits and keep it if the first misses. That does become likely in order to use cunning action and typical of actual gameplay. That gives the rogue 15.8 DPR with sneak attack.
3 rounds assumed...
Bard: 28+7.7+7.7=
43.2 (or 14+7.7+7.7=
29.4)
Rogue: 15.8+15.8+15.8=
47.4
The only rounds favoring the bard are actual fireballs. The only encounters favoring the bard necessitate a second damage spell or pretending sneak attack is somehow missing. A made save gives fireball less individual target damage than the sneak attack.
The rogue is doing twice the damage of eldritch blast. The bard's sustained damage sucks and he's trying to make it up by damage spells. Those spells have an obvious burst and AoE advantage. No one is arguing burst or AoE capability here.
That's ignoring things like the assassin's auto-crit and off-turn sneak attacks. A second sneak attack can be done up to once per round and all it takes is an AoO and standard sneak attack criteria. The only reason I was leaving it out was because it competes with uncanny dodge. 2 in the course of a day to match 2 fireballs isn't unreasonable. It's not like standard opportunities come up or effects trigger those after all.
You say you wouldn't use spells with concentration. What spells are you adding now in addition to the other spells you mentioned using? I've asked multiple times for you to post your build level by level to demonstrate how you are doing this.
His chance of a higher roll definitely goes up. That matters in the first round and helps give a fireball opportunity without friendly fire. "A lot" should be replace with "more than he does now" to be accurate. The rogue already comes with a good bonus from DEX. My bards typically have +2 from DEX at this level and +1 from JoaT's.
I have used enhance ability specifically for this purpose and find what you do with the initiative you win (or still lose) is more important than winning initiative was. Winning initiative a bit more often but giving up concentration is very often not as useful as giving up the advantage on initiative to cast a concentration spell in combat.
You need to post the build and explain how you're taking advantage of the tactic to back up the importance of initiative what non-concentration spells you are applying.
It's your rebuttals that are absurd. I calculated hit chance accuracy at 65% so "if he hits" is covered and no different from eldritch blast. The bard still has to hit too. Duh. Unless you actually didn't realize spell casters need to make attack roles too and those eldritch blasts also do no damage on a miss.
The rogue creating his own opportunity attacks can take some investment. Giving the rogue opportunity attacks or bonus attacks from another character is remarkably easy. If your bard wasn't doing damage he could use dissonant whispers easily enough (which I mentioned). Champions can give up an attack to grant it. The command spells works like dissonant whispers. Compulsion grants many opportunity attacks.
I had blended save and not saves as averaged out for fireball and since you don't seem to be on board with that I broke it down more for you this time. I was never leaving that damage on a save out of the equation.
You have a 15 DC save check. Chance to save 30% at no bonus or penalty, and increases by 5% per point of save bonus. You have a 1 in 3 chance of not dropping a standard orc with your fireball at 6th level to put that into perspective. Saves are made regularly at lower levels. Fireball or lightning bolt do damage on a save but not all spells do anything on a save at all.
Telling me my examples are absurd because of things I already took into consideration gives me the impression you didn't understand where those numbers came from. I have no problem with being wrong if you want to provide evidence. The problem is you never provide evidence. You just keep making unsupported statements and then repeat then like that will make them true, or attack arguments without disproving them. Or simply dismiss them because you make a statement and it must be correct because you made it.
Smart rogues do everything they can to land sneak attack. I choose to use TWF because the sneak attack accuracy rate goes up with additional attacks. That's just a basic understanding of the mechanics. It doesn't mean I'm a smart rogue, lol.
You are wrong, however; there are other ways to qualify for sneak attacks. Having another party member near is the easiest and most common. The second most common is anything that gives the rogue advantage. That's why people use the owl familiar trick as long as it remains alive. I prefer to be different and use animal handling for a mount or exotic pet -- either replaces a party member to be there.
Assassins automatically have advantage on anyone who hasn't gone in combat yet and auto-crits if it's surprise. Arcane tricksters can also pick up spells to pull it off, but the versatile trickster feature guarantees they can advantage by giving up the bonus action.
Sneak attack is easy. It's that second sneak attack (or third sneak attack for a thief at 17th level) that's takes more effort.
That's not true unless the chance to hit is 50%. The chance to land sneak attack is the chance to hit with that one attack. I've been assuming 65%, but the 14 AC your bard would have against the +7 bonus the rogue would be 70% for comparison.
Halving the number of attacks does half the chance to hit.
It's useful and situationally good. It's after the bard has more options that initiative becomes more important. The bards options taken have to match the situation they are in for that impact. That's why I said having concentration might be more important. The more options available the more likely winning initiative matters.
Damage vs 5e's high hit point opponents makes fireball more situational.
I don't take it. It's over-rated because I already have spells for mob control and the damage isn't that much per target. The "blaster bard" isn't a thing because warlock does the same thing so much better. I don't get enough secrets to add a damage spell when I have damage spells already in the pinch I might want it.
I don't even take the cantrip for damage because the crossbow bolt does just as much until 5th level and isn't far behind until 11th. By then I have better things to do with my actions than bad damage. I sometimes go with cantrip on a specific style but that's not what I typically do.
Which is why I don't both with the cantrip for damage. Whether the big spell is damage or not is irrelevant as not as it's useful. That gets back to my point that all you were doing was using hex instead of dissonant whisper and fireball instead of hypnotic pattern.
So does reliable talent.
The problem with that statement is it's reversible. The lore bard can be easily replaced. The skills are minor because 5e went bounded accuracy and removed niche protection. The rogue is essentially a martial class of another flavor so unless you are building the bard leaning towards evasive combat all you are only looking at one aspect of rogues. It's not just the skills, it's the complete package.