But from where I sit, mechanical stuff--which expresses how they play--matters. They're not just naked mechanics. The effect how things play out.
To a point, but only to a point.
I'm not sure if I'm coming at this from anywhere near the same angle as
@pemerton but I agree with what seems to be his basic conclusion: mechanical reflection of character differences has gained far too much focus as the editions have rolled on in D&D, at cost of differentiation in roleplayed personality, characterization, quirks, mannerisms, memes, and so forth.
I don't need mechanics in 1e D&D to differentiate these two Fighters at the table. They're the same level, both single-class, with the only real mechanical difference being that one is weapon-spec'ed and the other isn't. I've been playing them both on and off for well over 35 years, and both are still active:
---one is a practical-thinking generalist type, honourable enough not to steal but otherwise a greedy sort, who thinks his way through events as they come, who is fiercely loyal to those who are loyal to him and has no time for those who screw him over, and who - when given the opportunity - at least tries to do the right thing without seeking credit or glory. Currently he is trying to retire to somewhere quiet.
--- the other is a foul-mouthed get-outta-my-way swordsman with the diplomatic skills of a shoe who figures his weapon is the answer to every possible problem, that any sword he sees is his even if it's currently in someone else's scabbard, and that wizards are the scourge of the universe. He likes to be the center of attention. Currently he is trying to retire, build a castle, and make it an adventurers' base.
Even though they're close to mechanically identical, you'd be able to tell them apart within seconds were you at the table when they are in play.
And that's the point: if I can differentiate them that much just by roleplay, why do I need mechanical differences as well?