"Setting first" is meaningless. Meaningless.
That's a fine assertion, and it might be true for your game, but it's absolutely not true for mine. If it was, I wouldn't have an issue with floating ASIs.
A PC is not an average member of a race. They in no way define that race for the world.
Agreed. But the race that a pc belongs to should, and does (in my campaign), have a meaningful impact on the character.
I also, for the record, won't be adopting the new "pick your size" and "everyone lives the same length of time" stuff, either- because those are things defined by the character's race (in my game, and traditionally, too). Racial lifespan is a thing that significantly affects how the race acts and thinks in my game. Elves have a vastly different perspective than humans, and at least some of my players lean into that.
If it did, then 1 in 11 of every single race that gets a +2 could have a 20 in an ability score. Because that's the chance of rolling an 18 on 4d6 drop the lowest, plus your +2.
You're assuming that a pc is a typical representative of the race here- but that has never been the case in all of D&D's history. Pcs have always been depicted as above the curve. To project that onto rolling for stats, npcs don't get 4d6 drop one, they get 3d6 down the line, modified for race.
The flip side is that you are saying that while 1 in 11 have a 20 in some races, not 1 in 1,000, not 1 in 1,000,000, not one in the entire race could have a 20 if their ability modifier isn't +2.
...unless they're high enough level to have gained an ASI or have some other weirdness involved. Yes, correct. That's totally fine with me. It's a feature, not a bug. In fact, the aforementioned kercpa (Tiny squirrel folk) race that I have? Your maximum Str is not 20, it's 14. Other races in my game (though not the bog standard pc races) have higher or lower maximums in some stats than 20.
Because YES, you can play the outlier.
Sure. You can play, say, a gnome whose strength exceeds the gnomish normal. That is what you are doing if you have a Str of 12 or higher. And if you want to play the super strong gnome (for a gnome), you are doing so with a Str of 18. And if you really must have that 20, you can get there eventually- by putting ASIs into Str- but not as fast as a naturally bigger, stronger race.
That's part of being a gnome. You're not naturally super strong.
If you don't believe me, think about how so many people over the editions have wanted to play "the good drow" or other that plays against type.
Not having that extra +2 does
absolutely nothing to stop you unless your concern is optimization.
And I'm not talking about 20 to optimize.
You quite literally are.
To be clear, I'm fine with that if that's the game someone else wants to run. Have your fun your way! But I find floating ASIs to be extremely dissatisfying. I would probably feel differently if they hadn't been used to depict how far a race varies from the human baseline for, well, the entire time I've been playing D&D (since 1981).