Imo, and as others have said: racial abilities should be more defining if we're going to completely remove racial ASIs.
E.g.,
Powerful Build (Orcs) should grant Advantage to Athletics checks (i.e., Grapple, Shove) and +PB to damage when using melee weapons. Not the totally lame: "your carrying capacity doubles"...
Dwarves are pretty good already. Resistance to poison, stonecunning, and possible +1 HP/level are all solid character-defining features. Perhaps they should get Advantage in *all* Con STs, and *all* subraces should get +1 HP/level.
Elves should get a bonus to Dex (maybe just acrobatic) checks and a +PB bonus to damage when using ranged or finesse weapons (& spells?).
Gnomes are also pretty good. Adv on all mental STs is perfect for a "more cunning" race. Perhaps they could get a +1 to the Save DC of their spells and/or certain int & wis checks...
Tieflings should get more unique (non-spell) features relating to their heritage/blood/demonic features. Using blood to empower spells, moving their shadow or making their eyes glow red to Intimidate enemies, etc.
Small Races should get at the very least get Disadvantage on contested Athletics checks against larger creatures, and maybe a penalty to damage on melee & thrown weapons in exchange for +1 AC.
The above would retain the notable differences between the races (an Orc always does more damage/is more effective in melee than a Human) while still allowing for them to have the same stats and be effective at any class. Importantly, these racial abilities *shouldn't* be easily made redundant by class abilities or simply be "you know X spell."
* Optionally, replace any instances of "Advantage" with "Expertise" or "+ X bonus."
