So, I think this is pretty revealing. I honestly struggle to understand why people are so attached to racial ASIs, and so resistant to change, and the only reason I find persuasive is that it's just knee-jerk resistance to anything that smells of political correctness. Certainly none of the attempts at "logical" support for racial ASIs that I've read are very convincing.
Just getting this out of the way: I don't have a problem with dropping things like languages, proficiencies, or cultural features like Stonecunning from D&D racial traits. Those have been nagging annoyances to me for a long time. So let's talk about racial ASIs.
Set aside the arguments based on PC exceptionalism, simulationism (or anti-simulationism), or real-life racial history. Just look at the mechanics.
One of the PCs I've played the longest in 5e was a mountain dwarf warlock. Strength was actually his dump stat. That seems kinda dumb; I basically threw away what is probably the mountain dwarf's most compelling feature, but it was worth it to me for the medium armor proficiency, which would mean being able to forgo Armor of Shadows in favor of some other invocation. (And the unorthodox combo, including the fact that it
was unorthodox, contributed to an interesting story.) That's how the mountain dwarf is designed: no class that makes prominent use of Strength needs the armor proficiency, and conversely, no class that lacks the armor proficiency demands a high Strength. In nearly all cases, a mountain dwarf PC makes good use of one or the other feature, not both. The subrace presents a mechanical tradeoff.
Now, if I were customizing my origin according to Tasha's, it would be silly of me to have kept that +2 to Strength for a dwarf warlock; I should've, and would've, moved it to Charisma. Would that have made the character more compelling? No; arguably it would've been less so. Would it have had a noticeable effect on game play? Not much of one, if at all.
I often play nontraditional race/class combos, especially in 5e, which is really forgiving about it. Other favorites include a half-orc bard, and a halfling warlock. (Yes, I like warlocks.) In every case I have to think outside the box, since I'm not getting the most favorable ASIs for those classes, and that contributes to my interest in playing those characters. I find it much less appealing for all of those characters to have taken the +2 to Charisma. Personally, I think a world in which essentially every wizard has a +2 to Intelligence, and every rogue has a +2 to Dexterity, and every druid has a +2 to Wisdom, is a less interesting one.
Sure, I could just choose to place the racial ASIs in their traditional places, or at least not apply them to the most obviously optimal abilities. But that just feels obstinate, vs. selecting a race with assigned racial ASIs that don't easily fit with your class but making things work with other racial features, which is
interesting. Those kinds of tradeoffs are lost with floating ASIs. D&D races weren't designed for non-ASI racial features alone to impose interesting tradeoffs. They
could be, by expanding the design space for races (or lineages), in which case I might be okay with removing ASIs from them, but that's not the case now; every existing race would need a redesign.
Also note, for those arguing that floating ASIs make more race/class combos appealing: That may not be the case. It may be that it only makes
different race/class combos appealing. For instance, using Tasha's, I don't know why I'd play a perennial favorite (and classic) high elf wizard anymore; I get an extra cantrip, and some proficiencies I probably don't care about? Why not play a mountain dwarf; keep the +2 Con to make up for the small hit die, get a +2 Int (better than a high elf!), and instead of burning a slot on
mage armor, wear real armor, for an even higher AC. We'll see whether we start getting a lot more mountain dwarf wizards in our future. The change to floating ASIs doesn't make all races equally suitable for all classes.
My dislike of dropping assigned racial ASIs, given 5e's design, has
absolutely nothing to do with political correctness or the lack of it, and I find the assertion that it does offensive. It's about game mechanics.