None of these caricatures appeared here prior to the suggestion, nor has anyone really bought into them since, so I'm not sure you've set your sights on the right target here.
There is no real target, as I've explained in my very first post, Floating ASIs are an option, it's not likely that this will change and I'm happy with that situation.
After that, I'm just explaining why, at our tables, we don't allow them, not only to keep racial packages complete and as we think they properly represent the races, but also to avoid a bit more of power creep into the game, something that we have found does not increase our enjoyment of the game.
And—given all that you've shared of what you do and don't pay attention to at your table—it comes across that you see 5e as being to some degree modular for roleplay/story purposes. I'm surprised to see racial ASIs as such a sticking point for you to not possibly be a modification that can derive from the same intent.
As you can see above, it's not a sticky point, we are not using them, but from the start I've been clear that it's every DM's right to decide whether they want to use the option or not.
But it's exactly like us not using grids, it's just an option (and not only really too lightly designed - being an option - to make any sense), one that we just don't like.
I am curious of what you think of roleplay-heavy, rules-lite redesign attempts like:
Main Principles - D&D 5e Story Mode
Honestly, we are happy with the game as designed, it's flexible enough, heavily supported whether by DDB and all VTTs, etc. We are also mostly old time gamers who played AD&D, so 5e is really simple, simple enough so that when younger gamers (including our children and their friends) want to use them, it's not a problem to us.
Honestly, it's more in the way you understand the game and implement it and in the spirit in which you are playing it that you find the solutions.
That being said, we played for years (in particular when AD&D was in its second edition, that most of us did not like in itself, although the settings were the best ever) long campaigns of Amber DRPG, which is very much rules light (4 attributes, almost no rules and no dices), and we enjoyed that immensely as well.
But the fact is that it requires a huge amount of work for the DM just to create intrigues and follow them. Having a bit of combat that reminds us of the epic fight that we had in the past is not a bad things and it balances the preparation as well.
https://joelesko.com/dnd-5e-story-mode/main-principles
And with regards to the power gap again,
whether missed or glossed over, I'm still curious about the specifics of how you see floating ASIs increase this gap overall rather than reduce it and, at worst, create a handful of specific problem combinations?
OK, I'll go into the specifics with a simple example, the Tortle. I don't like that race, it looks ridiculous and you will never see me play one. And until Tasha, it was not considered an interesting option because although it's got fantastic advantages in particular for unarmored classes, its Racial ASI is in Strength which in turn mostly interesses classes that do wear armor.
But now that, thanks to Floating ASIs, it's an incredibly interesting option for casters, you can have a dream AC all the time without casting spells, and you can protect yourself even better with Shell Defense, emerging as a bonus action to cast.
When lots of caster classes are glass canons, you now have a perfect option for race that synergises really well, and you are not even stuck with a useless +2 to strength, so in the end, the casters (who honestly really did not need that buff) can be significantly more powerful than before Tasha.
Same thing with the mountain dwarf, by the way, where it can be even better depending on your dex, proficiency in medium armor and not hampered by the racial ASI of +2 STR. Or the Githyanki, etc.
These synergies really allow people to create characters more powerful (in particular by being far less fragile) than before the floating ASIs, at no cost to your technical offensive power.
And if you're already running with some modifications as opposed to purely by the books/RAW, why not address those specific combinations just the same in order to reap the best of both worlds—decreasing the power gap by improving combinations rarely taken under default rules and potentially increasing the breadth of the setting and story with those currently infrequently seen combinations.
We have almost no modification from the original game. In 3e, it was really a nightmare to keep track of all the house rules to prevent power creep, especially since we ran a multi-DMs campaign with at least 5 DMs who had to synchronise, so we said "never again". Fortunately, 5e is much simpler and the designers have understood that power creep is bad and will kill an edition in 4-5 years at most, so they avoid it like the plague. They still leave a few tidbits to keep powergamers interested, but put it as options, so it's really manageable if all you have to do is stick to the RAW and forbid a few options every 3-4 years...
Of course, if it all comes down to enjoying and leaning into provided archetypes like some others here, understood and so be it, but it hadn't stuck out to me as an important part of your stance yet.
It is, but because it's not an interesting topic here, being only personal preferences, I mentioned it specifically once or twice (especially when accused of racism wrt to elves and orcs), but it did not keep the attention up that long.