No, it really, really doesn't. For EXACTLY the same reasons that it doesn't work for Warlord. The base fighter class contains ZERO content that says "Swashbuckler".
Wait, what? Swashbuckler, to me at least, says a skillful swordsman. Dueling and TWF both back that up. So does Extra Attack. So, tangentially, do ASI's if feats are available. So do the BM's maneuvers if you go with that sub-class. The concept also says 'daring do,' which Action Surge, d10 HD, and Second Wind all at least help with, and, for once, even the Champion's 'Remarkable' Athlete doesn't seem entirely irrelevant.
Again, go down the list: (and frankly I'm ignoring the post where you cut and paste my post to make your point because it's too hard to read)
But, look at what a base fighter gets:
d10 HP
Simple and Martial Weapons
All armour
Fighting Style
Action Surge
Extra Attack (+1-3)
Bonus Feats (3)
Indomitable
NOw, what there says swashbuckler? A swashbuckler should not have d10 HP - he's not meant to take a beating.
hps represent avoiding physical damage by the skin of your teeth, too. The Swashbuckler is going to all but live in melee.
It's superfluous. In 5e, it doesn't matter if you have heavy armor proficiency - if you go high-DEX and light weapons, you're in good shape. Where armor proficiency might make a difference is if you don't have the best light (if going DEX) or heavy (if going STR) armors on your list.
Fighting style - well, I suppose two weapon style kinda/sorta fits one style of swashbuckler. But, the rest of it? Why is my swashbuckler good with shields? Or good with bows?
He's not, you pick the one (or two if Champion) style(s) that fit the concept.
Action Surge? 1/short rest bonus action? Woo, nothing says swashbuckler like being able to be quick once every few hours.
it's better than never being able to be quick.
Extra Attacks? Maybe, I suppose I can see this. Weapons master and all that.
A perfect fit for the lightning-fast rapier-wielding duelist. And, it's the Fighter's single most potent, most significant class feature.
Bonus feats? Considering most bonus feats have nothing to do with swashbuckling, it's pretty moot.
And feats may not even be available. Swashbucklers - like most genre heroes - tend to be pretty all-round gifted, though, so a couple more +2's'd be welcome.
Indomitable? Bwuh? That's nothing a swashbuckler should have at all.
Not as emblematic as being great with a rapier, no. But really the only thing that's less than a good fit and not a matter of choosing something else that is.
Compare with the 5e rogue swashbuckler. Base class gives us the following:
d8 HP - perfect fit
d10'd be better if you're going to melee a lot, but it's OK. Really, no one's that hard up for hps in 5e that 1/level on average is huge either way.
Light Armor - perfect fit
Even light armor's a little off the classic Three Musketeer's look, but by D&D standards, sure.
Sneak Attack - Perfect fit
Not quite, perfect, no. Swashbucklers are really into dueling, where getting advantage isn't the sure thing it can be for a Rogue working with teammates.
bonus Action - Perfect fit
Nice for specific bits of daring-do, yes, not so good for going to town on the Six Fingered Man.
Skill bonuses - Perfect fit.
The fighter is sadly lacking in skills compare to the Rogue, and the Swashbuckler does quite a bit of skillful stuff, so yeah,
Why on earth would you create a swashbuckler as a Battlemaster?
Hello, my name is Inigo Montoya, you killa my father, prepare to die.
The base rogue fits every swashbuckler requirement to a "T". Add in some sub-class goodies to further tailor to the archetype and we're good to go. And, oh look, it worked perfectly well. We've got a swashbuckler rogue sub-class that works very well. No squinting or ignoring large swaths of a class required.
We've got both. That a fighter could cover some, less skill-focused, more melee-focused swashbuckler concepts was never a reason not to do the Rogue archetype, that shaded towards the opposite emphasis.
At bottom, the Swashbuckler is a character who crosses swords with the bad guy and wins. In D&D, that's modeled with melee DPR, and it's a big part the classes that get it.
The fighter and rogue both fit the bill. If you're not all about dat damage, neither of those classes are such a good fit.
It's like people look at Totem Barbarians and try telling other people that Druids aren't required in the game. After all Totem Barbarians can talk to animals, why do we need Druids. We got the animal themed powers, talking to animals, it's a Druid, so, people who like druids should just sit down and shut up and play Totem Barbarians. And then acting in wide eyed bafflement when people start asking to play actual druids. Actually, worse than that, trolling every single discussion to create a druid class by loudly proclaiming that everything you need to create a Druid is already in the game and anyone who wants an actual Druid class is just a munchkin power gamer who doesn't understand D&D and should go back to playing another edition and stop trying to bring things into 5e that don't belong.
It's ludicrous.
It is. It misses how 5e gives you multiple paths to similar concepts, and asserts that one path to one concept in the ballpark obviates all others. It is ludicrous, but you don't have to pretend a DEX-based fighter can't buckle some swash to make that point. Quite the contrary.