@doctorbadwolf
I know you think floating ASI's won't cause players to fall into playing "their favorite race" for everything, but I wouldn't be surprised if a fair number did. I mentioned before one player in our group who plays dragonborn a LOT.
To be fair, I certainly believe those players (who stick to one race) will be a small number. But as it has been said, if they can play a race they love to play and not feel like it is subpar to other choices, what is wrong with that? Personally, I would see such behavior as a lost opportunity for the player (like I've encouraged our Dragonborn player to try other races and he has had fun with them, in particular loving his Gnome!), but I certainly won't fault them for playing a race they really enjoy.
In a similar light we have another player who plays monks and paladins almost exclusively. I told him for the new game I hope to run later this year, I
really want him to at least try another class! I told him if he simply isn't enjoying a new class, I'll let him remake his PC. So, he agreed and I'll be anxious to see how it works out.
Over all, I think (if we
insist on keeping the ASIs), floating them is the least of all evils. Remove them from race and just add them as the end part of determining your attributes. You can float them to whatever ability score you want for whatever reason. You're Paladin is stronger? Ok, sure, why? Because he is a Dragonborn, because he has a Solider background, or just because he is a warrior? Honestly, does it really matter? You can come up with any reason you want.
In the light of the halfling/orc comparison. Both are barbarians, both used point-buy for max 15 STR and added ASI +2 for total 17. Maybe the orc's is just genetics due to race, maybe the halfling's is because of his barbarian "training" (?) or his Far Traveler background? Thematically, you can reason it out however you want.
Finally, what I
still have issue with, personally, is more about encumbrance and other physical factors related to races. In discussing this with our newly budding DM last night, he was shocked to learn Medium creatures don't have advantage over Small for grappling, or that small creatures could carry just as much via STR as medium. To me, ASIs are secondary, some of the other issues are really the points that break verisimilitude for me.