I think it'd be nice if ability score increases came from a mix of race, background, and (maybe) class. Representing inborn (or cultural) traits, learned skills while growing up, and initial class training.
E.g., a half-orc gets +1 Str; a dwarf gets +1 Con; a full orc gets +1 Str/+1 Con/-1 Int; a gnome gets +1 Int; humans get +1 to two stats and -1 to another stat of choice; etc
An entertainer gets +1 Cha, an acolyte gets +1 Int, a hermit gets +1 Wis
A fighter gets +1 Str or Dex, a Wizard gets +1 Int, a Bard gets +1 Cha
This would:
- make background more important than it currently is
- retain differences between races (you could alternatively remove the ASI from class and make races give larger bonuses, still leaving race+background as sources of ASI)
- provide much more flexibility in Point-Buy builds, as you only need a single +1 in order to get 16 in a stat. So it'd constrain only *one* of race/background/class, allowing you to play a ~fully powerful half-orc wizard, but who has by default more strength than an elven wizard
Alternatively/in-addition: Potentially racial ASIs should add to stat caps. An orc has a natural str cap of 22; a dwarf has a Con cap of 22; an elf has a dex cap of 22, etc. This retains the effect of racial traits, but doesn't punish "off-race" combinations for starting adventurers. Because yes, a gnome that has trained for 20 years should be able to start out level 1 with 16 strength. They have worked hard to become strong; *however,* eventually they'll run into their racial limits.