Start looking at bard dice as additional like level 1 spells that refesh on short rests.
Why would I do that? It's an arbitrary analogy. I did that with 3.5 spell songs because fascinate, suggestion, and inspiration came earlier and were potent. There's a direct comparison with suggestion as the spell and suggestion as the song to validate it, and even better songs like freedom and mass suggestion later that correspond directly to spells.
Bardic inspiration is better than guidance but more limited because it's not at will, and behind spells like bane or bless with because of their durations and multiple targets even with similar effects. 1d4 on 3 targets for 2-3 rounds is much better than 1d6 on one roll 3 times per day, which is where we're really at initially.
Eventually 5 dice at d12 per short rest after scaling up is better, but it's really more comparable to the 6 dice at d12 per short rest expertise dice with more options from which to choose that battle masters get. Unless you're about to tell me battle master maneuvers are the equivalent of 1st level spells I think your argument falls short here. ;-)
Cutting words more or less functions as a shield spell that you can stick on other people. And that's just one use.
Shield lasts a full round and provides the benefit to multiple attacks while cutting words is only good against 1 attack. +5 is a high roll bonus until cutting words gets up to d10's at 10th level. Shield also has the situational perk of blocking magic missiles. Immunity to charm doesn't prevent shield like it does cutting words. +5 AC against multiple attacks is better than a die roll against a single incoming attack.
At level 3 it's more or less 9 extra level 1 spells you can use as reactions.
At level 3 the bard doesn't have font of inspiration so it's only 3 times per day and it's still a d6 so it's a -3 penalty to attacks compared to a +5 bonus to AC that you're applying a false equivalence on top of the other advantages shield has over bardic inspiration.
At that level, a shield that's blocked 4 attacks has outdone the entire day's worth of bardic inspiration, and it's more likely to block attacks.
Since you are using shield to try and compare, just take a look at spell mastery. Shield at will. This is because the wizard chassis supports casting additional spells, unlike the bard chassis, and this is comparing the base class to your uber subclass example. That's not even adding in wizard tradition benefits.
The bard us primary spellcaster comparing it to average damage from rogue is a bit silly.
What's silly is it's an argument without context or demonstrating how it refutes my point. The rogue skill benefits come online earlier than the bard benefits, the rogue has more proficiencies, and the rogue has combat benefits built into the class bards don't.
Are you comparing d4 vicious mockery to sneak attack when you say primary spell caster damage is better? Because bards don't have good damage spells, and they don't have room to add them while continuing to "do everything" as has been suggested.
They can also steal those broken spells in the Paladin and Ranger spell lists. Destructive Wave 7 levels early with hex, fireball and Eldritch blast.
So a 5th level spell is really a 9th level spell just because a paladin is a half caster? Sound legit, lol. Spells are ranked by spell levels and not class levels so your argument is extremely flawed here.
Or take fireball and healing spirit level 6.
Well, one subclass can. Bards cannot. The real question is what did the bard not take to get that? For starters, no AC boost. Next, no eldritch blast, hex, or hunter's mark. They only got two so sustained damage is given up to become and better healer and fodder killer.
The next thing to really consider is how does that make them better than any other caster who has those spells one level sooner? Casting healing spirit didn't make it heal more than the druid does, and fireball doesn't do more damage than the wizard did. The wizard can cast more fireballs, however, because the class supports casting and adding a subclass geared toward that type of spell is going to open up evoker for better casting of the same fireball as well. Or a sorc could also cast it a level earlier and better with metamagic.
The last thing to consider, is that the spell slots are already available for hypnotic pattern or fear or any other good bard spell already taken. Adding fireball when the bard is likely going to cast hypnotic pattern with the slot anyway doesn't make fireball somehow more powerful either.
So yeah they can match rogue damage at range with hunters quarry/hex and Eldritch blast. Plus they can drop fireball.
That's 3 spells so we're at 14th level bards or 10th level lore bards. Presumably the 4th spell is healing spirit because you're trying "to do" everything with this uber bard.
So think about what you are giving up again. The destructive wave argument went out the window having taking those four spells. Considering destructive wave is 10d6 in a 30' cone with prone and fireball in the same slot is 10d6 with a 20' radius and more commonly resisted damage type. Personally, I think the range and AoE wins out over conditional damage type benefit and prone. In either case it demonstrates why "7 levels earlier than a paladin" is meaningless. It's still just a 5th level spell that your examples replaced with fireball.
It also presumes the bard didn't take a great 5th level spell like animate objects one level earlier. Or important healer spells like mass cure wounds, raise dead, or greater restoration. This gets back to the point on about what the bard did not take in order to take the spells in your example.
That 10th level bard knows 16 spells going lore per your example. Technically 15 because you gave one up for a cantrip. That's spread across 5 spell levels. That's not that bad, but it still forces choices, and it's on the cusp of the massive slowdown in new spells know that hits known spells casters in the 3rd tier.
Hex and hunter's mark kill using your concentration so you either don't have that damage or you don't have the use of those other spells. Like hypnotic pattern. Just because a spell comes from another class doesn't make it better than the spells of the same level within your own class, but the compete for the same spells known and the same spell slots.
Getting back to damage, we're looking at 2d10+2d6, soon to be 3 and really it's not a bad way to pick up damage. The 10th level rogue thief has 5d6 sneak attack (soon to be 6), plus base weapon damage 2d6 TWF, plus DEX mod +5, plus fast hands ball bearings trying for prone and advantage for more accuracy (decent enough chance even without high success). Sneak attack itself is fairly easy so if we're going to assume the hex isn't lost to a concentration check or given up to a useful spell then we're going to assume something as easy as sneak attack also applies.
That still looks like the rogue is ahead in damage to me at 10th and 11th level. Like I said, bards make an investment to catch up and still remain behind. Probably better off to cast dissonant whispers and trigger the AoO and extra sneak attack for the rogue. No magical secrets needed for that at all.
Rogues take a bit long to come online.
Expertise, sneak attack, cunning action, uncanny dodge, evasion? What's your reasoning for coming late online? Their best abilities are in the first 2 tiers of play and then they get reliable talent.
Cantrips, the argument you gave for damage, are the epitome of coming online late. Bardic inspiration starts off per day and requires CHA ASI's to build up, and the dice take a while to scale up. That's taking a while. Magical secrets doesn't even start until 10th level in the class.
Magical secrets are extremely over-rated. They can add nice options but all they are doing is taking the place of the other nice options that already exist in the bard spells. It's can add some flavor or versatility so it's not a zero sum exchange, but it's not the game breaker people make it out to be. Not even remotely close.
Bards are fantastic support and can fill in other areas. Definitely not a "do it all" class.