That said, I struggle to understand why there is such a push in favor of the subclass design, which incentivizes multiclassing.
I feel like pushing subclasses to level 3 in 2024, outside of theory crafting level 20 characters has mostly put a stop to multiclassing based primarily on subclass abilities at actual tables. Most multiclassing now is for armor, particular low level spells/cantrips, or when a class like ranger and to a lesser extent class abilities like rage or monk's martial arts. Maybe after level 5 on some martials it's still around because their class features are pretty bad after that. Not true of Fighters, Monks, Paladins. Barbarians are right on the borderline.
If feats were more interesting, it may be possible to have more builds which are single class + the right feats rather than multiclass, or at least MC with fewer number of classes in them. Why is it so frowned upon to have options for "lightweight multiclassing via feats"?
IMO, Feats are very interesting, you just don't get enough of them as is, let alone if trying to add in using them for lightweight multiclassing, which due to the current design will ensure that at best this will be good for a few classes and bad for all the others.
Having more interesting feat options could also lead to more players choosing them over ASIs, and accepting that they won’t have any stat at 20 by 20th level.
We are already mostly there. For 2024, most characters in 1-10 level range (most played range) are choosing feats ahead of ASI's.
I think the big problem is looking to level 20. That's not where the game is played. Except as an intellectual exercise those levels really don't matter.
With current 5e rules, it’s almost guaranteed that any moderately optimized character has 20 in at least one stat, and maybe even two, by 20th level. Why is such sameness and homogeneity considered ideal? In the name of simplicity? Maybe it’s too complex if builds aren’t all mostly the same? But I thought the big fear of having more feat options was that it inevitably led to sameness

… well, if sameness is already what we have anyway, then why does it matter?
Part of the issue there is that players are shoring up major class weaknesses with their feats. Casters taking Warcaster because concentration. Martials taking mage slayer because weak wisdom saves. Often Martials taking a damage increasing feat because their damage is fairly anemic otherwise (especially compared to casters using spirit guardians, moonbeam, conjure animlas etc).
Essentially the structure of the game as is incentives using feats not for thematic reasons but to fix major class deficiencies. And your right there aren't many feats to shore up those deficiencies. But what this means for the current state is that all these feats you want to make aren't going to be used unless their similarly as useful (in which case you don't really need prereqs or feat chains), and they will only possibly be highly useful for a small subset of classes - striking down the primary purpose you wanted them for at the beginning (as universal prestige paths / feat chains).
I'm fine adding more feats, but there are pros and cons for the game design embracing feat chains/prestige paths using feats/mutliclassing using feats and for me those cons outweigh the few pros we might get. Almost everything that you want to achieve can be acheived by making stand alone feats and allowing the player to freestyle pick them as they already do.