I think we are agreement in here that issue is some specific combinations of mechanical features, especially along with questionable fiction, not the concept of fantasy species having differing capabilities in itself.
I think 99.9% of people even in the Wilds of Twitter, are. It's just they need to avoid really negative stuff, and sometimes it's worth sacrificing some arguable verisimilitude for simplicity, I'd say.
I feel they're consistentish, but of course there is a lot of simplification and abstraction in a game like this.
I really quite strongly feel like they aren't, and that in fact the six abilities D&D has don't really cover a lot of stuff, but they still want to assign one for mechanical sake, so it gets jammed into one, but YMMV.
But of course the changes to races affect balance too. Like how in previously you couldn't combine the dwarven armour proficiency (useful to casters) with optimised casting stat, but now you can. Furthermore, I really see no significant difference between sapping racial features and swapping class features. In either case what the character ends up with is changed.
This is a literally irrational/illogical argument. "A change" isn't the issue. Balance is. Balance is always, always, always, always, always a measure of degree (that's literally what it means), not an absolutist "Was there a change yes/no". The minor changes you can make with free ASIs only improve balance and predictability from the design side, as I noted. They're actually a balance positive (from the design side, again). You can't "swap racial features", you still have to pick a package of abilities. Are some better than others? Yes, but that was already the case. What's different now is people have far more flexibility as to which package they choose, because they don't need to also align the ASIs.
As for Dwarves specifically, I think they're going to get nerfed with DND2024. Right now, they're in a sort of beta/limbo state, where they can adopt the unfinished/unbalanced Tasha's rules and that's kind of advantageous to them, but if you saw the changes to races with the new monster book, many were pulling races up, power-wise (at least arguably), quite a few were "neutral-ish" (but basically positive) and a handful were nerfs to outliers. Mountain Dwarf is one such outlier and when we see the 2024 PHB, will likely get the same treatment (maybe we'll see it even earlier).
You can't mix-and-match racial features either, which is what you were suggesting with classes. Anyway, again balance is not binary. It's a matter of degree - and being able to change classes significantly would have vastly more impact that this does, and that's only going to become more obvious with time as the PHB races etc. get pulled into line.
Yes, in fantasy you can justify anything. But if you use that that flexibility of fantasy to justify why everything has identical capabilities in everything despite drastically different sizes and physiologies than that to me is an utter waste.
And yeah, I agree that the size should affect more things and there should be more rules keyed to it.
Re: justify, sure, but that's just aesthetics. That's just taste. It's not a rational argument that something needs to be a certain way. It's not even an argument for verisimilitude, because there's no consistency that Halflings are weak, in fact, through five+ editions of D&D, Halflings have always been shockingly strong for their absolutely diminutive size (literally the same size as an average 5 year old). Making it so they're 100% as strong as a human, instead of 95% as strong (literally the pre-Tashas 5E situation thanks to the human +1 across the board - in 1E is was 94.5%) is just not "breaking verisimilitude". That 5% gap closing might aesthetically offend you, but that's not meaningful verisimilitude. Even to call it a fig leaf would be too kind.
At some point, you need to recognise D&D is not a simulation, so the value of verisimilitude must be weighed against other factors. Sure, we could have special rules saying "Halflings can't put their ASI points in STR" or the like, but that sort of thing will just lead directly back to the problems D&D had before, as someone decides that Borcs (who are not orcs) can't put their ASI points into INT and suddenly thinks start looking unfortunate, and it just complicates matters to no useful end. It's such a tiny and arguable "benefit", and it's an utterly needless complication.
Whereas size rules could offer some meaningful verisimilitude. They could also be consistent, and with a number of races, people could opt in or out of them.