Note, I never said that alignment is a legacy thing. To be fair, in 5e, it largely is, but, that wasn't the legacy bits I was pointing to.
In earlier D&D, monstrous races were extremely unbalanced. Particularly in pre-3e, but, even 3e had all sorts of issues with trying to balance races for play. So, often the notion of "this race is hated" was used to balance the totally unbalanced mechanics.
And it doesn't work. Either the DM flat out bans all monstrous races because he or she doesn'T want to deal with the mechanical imbalances, or the "this race is hated" stuff gets left by the wayside because no one at the table really wants to deal with it.
My point was, trying to create mechanical balance with role-play elements is a failure. It just does not work.
Now, every situation is going to be different. There is no blanket right answer here. 5e races are, largely, mechanically balanced. Again, no one is playing a goblin to "get more power". I think it behooves the DM to know his players and talk to the player about how much that player wants the race choice to matter in the game. Maybe he just thinks it's cool to play an Aaracockra. Not that he wants to power game or whatever, but, he just wants to be Hawk Man. Cool. No problems. Wasting excessive table time on stuff that the player has no interest in will just result in unhappy players and a garbage game.
If the player wants to play up the monstrous aspects? Fine, no worries. If the player doesn't want to play up the monstrous aspects, that is ALSO fine and no worries. IOW, do what is actually fun at the table.