Before I dive in, a few corrections on past matchups:
On Mediator vs Archer: I totally overlooked this at the time, but Mediator was literally the only class left that could use Robes. Between White Robes and Chameleon Robes that's actually a pretty big deal. Further cements Mediator as the correct choice there.
On Archer vs Dancer: I listed Archer as having the higher damage physical attack, but in reality I suspect that honour actually goes to Dancer (at least...post-Cachmere pre-Gastrifitis...although they pull into first again post-Gastrifitis if you grab the common-poach Ryozan Silk). I don't think this is enough to tip the balance--everyone still uses Charge, Concentrate, and Arrow Guard all over the place. Archer still has the best HP, making them an attractive carrier. Archer still brings Shields, which break some fights. Archer still has range on their damage. Dancer still has the gender restriction. But...it certainly makes things closer.
(a) Thief > Bard for a chapter and a half by virtue of existing.
Yeah, I'm a little hesitant to go along with this logic for the following reasons:
Suppose the two classes left were Thief and another high tech class--let's go with Samurai. Would Thief win that just because they win almost half the game "by default" and are still somewhat relevant during the rest of the game?
Let's go with an example from another angle. Let's say the two remaining classes were Archer and Bard. You'd go to Archer first, grab a few charges, think you yourself "should I start unlocking Bard yet?" and then conclude "naaah, let me get Concentrate first--that's going to help regardless of class". Then when you had Concentrate you'd go "Ok, should I start down the path to Bard now?" and then probably react "wait, wait, I'm going to want Arrow Guard anyway, and it's going to make a huge difference--let me get that first." And then, only after you've gotten 1500-2000 JP worth of abilities, do you go "Ok, sure, I guess I might as well unlock Bard now."
By comparison, when it's Thief and Bard, you...grab Steal Heart, and then ask yourself "ok, should I go unlock Bard now?" and...the answer is...probably yes. What are you sticking around for? Move+2? You're only going to replace it. Secret Hunt? Not relevant until Chapter 4. Maybe get it on one person just in case you run into an Ahriman at Fovoham Plains or Zigolis Swamp or Zerekile Falls or Barius Valley or Mandalia Plains (Ahriman have Air Knife as their rare poach). But you don't need Secret Hunt on more than one person for the random Ahriman. Caution? Meh, unlocking Bard will probably help you more.
Add to this, what's the best time to unlock Bard? Probably Chapter 1 when you can lean on guests. At least if we're going by SCC-style guest rules, Chapter 1 has likely become the easiest Chapter.
I guess what I'm saying is this: the competition in Chapter 1 isn't between Thief and Bard, it's between Thief...and heading down the Bard unlock path. And I'm actually feeling like the Bard unlock path is the better choice.
This doesn't exactly mean that Bard wins Chapter 1. The best analogy I can think of...let's say in a normal game of FFT you learn Magic Attack Up pretty early in the game. You're still going to use Gained JP Up in 75% of fights, but you might pull out MAU in the 25% of fights that are actually hard. Similarly, Thieves with knives and Steal Heart are still better than Mediators with knives and Steal Heart, so you might pull out the Thieves in a hard battle. But it's only a slight upgrade, so you'll try to squeeze by with Mediators whenever you can (much like Gained JP Up).
Chapter 1 feels like a wash to me.
I think you may be underrating Steal Heart a bit. Sure, Steal Heart is mediocre... when you have the ability to blitz safely and effectively. The Thief SCC doesn't, nor does the Bard SCC, and I doubt the intersection of the two (with Mimes lategame maaaaybe) is much better.
Actually, they are rather a lot better. If you can run away for two turns (and you have 7 move: you almost always can) then Battle Song goes off three times per user. 15 Battle Songs is an average of +7.5 PA...but it's actually better than that in practice because it's random and fists are quadratic.
In Chapter 2, when your PA starts at 7, using Battle Song for two rounds (3 activations) raises you from 35 damage on average, to 147 damage on average.
In Chapter 3, when your PA starts at 14 (thank you Bracer), using Battle Song for two rounds (3 activations) raises you from 140 damage to 325 damage on average.
What if you only have one turn of prep? If you're speed 6 you can still pull off two activations of Battle Song in a single turn. Still enough, in Chapter 2, to raise your average damage from 35 to 99. Still enough, in Chapter 3, to raise your average damage from 140 to 251.
You can't really do this on the Bard SCC. Or rather, you can, but you need to spend a couple turns just to bring your PA to Thief levels, and THEN you can start making yourself powerful. There's not much point to doing this when you have Red Chocobos--one Battle Song promises ~70 future damage (spread across five units) while keeping your distance from the enemy. Choco Meteor deals ~70 damage
right now, also while keeping your distance.
On the other hand, Steal Heart is very dominantly useful when your slugging ability is poor. (As such I don't think you'd only have one female, for instance.)
I'm actually entertaining the opposite possibility: whether 0 females is the correct party composition. In any fight that isn't a total blitzfest where you can run away for at least one turn, I'm pretty sure Battle Song fists becomes the dominant strategy. Females can't sing, are worse at punching, and don't get Move+3. All this for a slightly better version of Steal Heart?
(b) Later on, thief still provides Steal Heart, and up 1-3 Chantages depending on taste.
Yeah, I'm not inclined to give a whole lot of credit to the 4-Chantage party. It's something you only get by beating the deep dungeon, and then repeatedly fighting a battle that spawns only one Porky on average. And then you get to use this party in...six whole story fights. I mean, yes, it makes a decent case for being the strongest party you can field in those six fights (even though it can still lose). But it's not really centralizing. Now, what it DOES stop is anything else becoming too centralizing during the last six battles, because "grind for 6 hours and get Chantage Cheese instead" is always a viable counter-option.