Let me put it another way: How do I avoid min-maxing a character's ability scores without engaging in circuitous reasoning? By which I mean, I choose how to allocate my rolls, and as a roleplayer, I choose to allocate those based on the character I'm making, rather than pure statistical consideration... but I'm still making a wizard; a half-orc wizard who ran away to candlekeep as a teenager... so I put that 17 I rolled into his Int, to express the fact that he's spent his teen too adult years exploring and enjoying a love of learning that he wasn't able to express in his home tribe, and really dedicating the whole of his time and effort to that. Next, I'll put the 8 I rolled into his Constitution, to represent the fact that he's really not looked after himself physically in the intervening years, and stay sup too late, doesn't get enough sleep, and has generally given himself a less robust immune system from his cloistered lifestyle. I'll put the 14 I rolled into his Dex, next, because even though he's not particularly active, his reflexes are still fast, and his hand precision has been kept up with a lot of fine manual work managing scrolls, sorting catalogues, and truthfully his data entry speed is pretty exceptional at this point. Next I'll put the 10 into strength, He's carrying a lot of books about most of the day, but he's not really working out, not to the extent that the lifestyle in his home tribe would have seen, and his general muscle mass is a pale shadow of what it might have been. I've got an 11 and a 12 left, I'll give the twelve to Wisdom, and the eleven to Charisma - he still retains some of his basic survival knowledge and his senses are sharp. In particular he's grown accustomed to listening for slight and small sounds in the expansive, generally very quiet archives. Meanwhile, he's passably social, and able to communicate what he needs in a friendly manner to his colleagues, but it's nothing to write home about. Not a shy and silent wallflower, and not really a big socialite either.
Now... where do I put my plus 2? And, more pointedly, what reason do I give for putting it somewhere that isn't just a direct repeat of a reason I already gave for a particular stat allocation? How do I place my plus 2 and plus 1 in a way that is motivated in character, but not just doubling up on an existing character element? How, in a way that doesn't conflict with or negate one of those elements? How, in a way that is not purely game-talk mechanical "this because it's my casting stat and I want it high" or "this because that will bring up this modifier by one and even it out"? Explain how this helps a roleplayer, rather than hindering them by pushing them into making game-centric choices based on min-maxinig rather than character?
You put the +2/+1 where you want and you modify the justification as needed. It’s absolutely no different from how you justified the explanations for the other ability scores. No matter the method you allocate your scores, even if you aren't using floating ASI's and are leaving the original default racial ASI's, you're still doing the same thing in the same way. The key point is that the numbers and where you decided to put them came BEFORE the justification.
You're arguing that floating ASI’s pushes players into making game-centric instead of role-playing-centric choices, but do you not think that fixed racial ASI’s
also pushes players into making game-centric instead of role-playing-centric choices? Because it does.
Yes, our differences should be celebrated, but letting players allocate their stats doesn't wash away racial differences the way you seem to suggest. Tieflings still get their spellcasting and fire resistance, half orcs still have Menacing, Relentless Endurance, and Savage Attacks. Proficiencies are great way to express many of our differences culturally, but also things like the Goliaths Stone's Endurance show us that even the Goliath that lived cloistered as a wizard is still a very durable and hardy individual. Elves still get magic in a way that others don't with free teleportation from some options or cantrips from others to show their natural magical heritage. I would even go so far as to argue that being able to use those differences on a different style of character from the racial norm can easily highlight the differences in just the traits. Halflings are still lucky, Dwarves still get poison resistance to show their constitution, Vadelken still resist effects targeting their mental saves, making a Vadelken Barbarian a more unique Barbarian because it also gets mental save advantage from its heritage despite being a person who lived their life eating raw eggs and lifting heavy things while getting very angry. Going into stats to say makes races are different is very shallow thinking in my opinion since by moving stat increases you provide more opportunity for those racial traits to shine through.
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Your racial differences are better expressed through traits, not stats, and that's because your characters stats should reflect their lifestyle choices, not their born heritage. WotC is not washing away racial differences, they just aren't doing a good job of giving new races distinguishing features. It is a races general lifestyle that has dictated their stat blocks previously, not the races born characteristics. Even before Tasha's I always thought of racial ASI as little more than indications of the races societal lifestyle and cultural differences over being literal racial differences. Not all Half Orcs are bumbling and brutal oafs, not all Tieflings are charismatic folk, not all elves are elegant and graceful, just that the majority of them are, and being different from your race should also be good. One might even be able to say that being a member of a race that behaves different because of their stat blocks should also be celebrated along with their racial differences from other races. He is his own race, but he is also still himself and not one of a hivemind.
Yeah, all of this.