On that thread about non-martials having a rough time getting new weapon proficiencies which scales past Trained, had me thinking of the ①titular question, and the following derivative:
②Is having multiple martial classes with strict niche protections on the availability of individual fighting styles worth it for the game?
The fact that when another game, the often ill-spoken 4th Edition of Big D, divided classes into power sources, had a single Martial source manage to cover all classes that weren't Arcane, Divine, Primal, Psionic (4E's probably-equivalent to PF2's Occult), and Shadow, also cements this personal suspicion that weapon based fighting as a whole being divided among classes might be harmful to both the martials themselves and spellcasters.
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P.S. Just in case, while the question may seem adversarial against martials, I actually prefer them to spellcasters (due to underdogma, I admit though).
1. Is weapon usage cheaper than spellcasting? No.
Neither is cheaper in that both cost you your class choice.
Do you want a martial chassis w/ weapon usage?
Or a full caster chassis w/ full casting?
(I'd place Alchemist in the latter category.)
In the same vein, a max Int PC w/ Rogue Dedication would struggle (and fail) to catch a dumb Rogue in skills & skill feats.
Your PC can cross 1/3 of the way over via MC Dedications (though War Priest does some of that work for you.) A full caster that wants to go martial cannot catch up to a martial class, nor vice-versa.
They're likely better off taking Polymorph spells for when they get that urge (and buffing Con to survive.) I'd say Summon too, but the creatures are questionable, and more like h.p. sponges.
Arguably it costs fewer feats for the caster, but there's more than weapons alone. For armor, efficient combat tricks, & h.p., they'll need more feats like the Dedication Resiliency ones, which still don't catch up completely. And they'll be behind on when they unlock cool martial tricks (if ever for the later ones).
(Yes, one can burn lots of their spell slots to get a semblance of similarity, but the martials have "unlimited casting" so...)
On the flip side, it's difficult to be bad at your class's shtick.
You can dump your casting stat and you still get as many spells as the maxed out guy, it's just you should avoid offensive spells.
(Funnily enough, a MC Ded has a higher stat requirement.)
And a martial who maxes out their attack stat, even in a sub-par race/Ancestry, can do just fine no matter the feats they choose.
This in turn leaves everybody with lots of room to explore MC Dedication options with few worries, as well as some of the odder class feats (partly because there are fewer feat chains).
2. I disagree with your premise. Most martial classes can be built for most fighting styles.
With Dedications, the only insurmountable niche is Rogues having Dex-to-damage, but IMO that's not a style. Finesse fighting works fine for the other martials too, they just can't dump Str like a Rogue can.
When I think of fighting styles, I see them as available to most classes. Ex. Two classes are awesome at sword & board, yet shields are solid enough and cost only a General Feat. Imagine a Barbarian protecting all that h.p. with a shield? And it doesn't hurt their offense any more than it does the other classes. And many martial classes have an alternative source for a circumstance bonus to AC.
Most (sometimes all) of the martials can be good with big weapons, reach weapons, TWF, ranged combat, mobility, tanking, Reactions, finesse weapons, agile weapons, and/or maneuvers too. Most with little investment. So yep, can't say there are locked niches.
Heck, an 8 Str Rogue has the luxury to get Expert/max Athletics & Assurance and use their last action to knock down a sizable portion of their at-level foes automatically.
And a Fighter archer plays differently than a Ranger archer, but that's pretty cool given that their damage stays comparable. So even though most of the classes can be built toward most of the styles, there's still a different flavor that makes them distinct at the table.
Cheers