"Playing against race" is really a more polite euphemism for playing a gimped character though. It might be interesting, but I really don't think that is enough justification for making some races worse at some classes / playstyles. Player freedom simply has to trumph in this consideration, as far as I am concerned. Racial flavor, as far as I am concerned, should be just that; flavor. Not mechanical advantages or disadvantages.
You're allowed to want that for your game and have that opinion about playing a gimped character. Not everyone does though.
Originally Posted by Sozz
If we could make a system that gave different mechanics to every race for every check they made, that would be incredible, orcs get +4 when lifting objects, halflings get advantage when locating pork pies by smell, but without covering the world in leather we cover our feet and those situates are consolidated into the Ability score system, so that every situation undefined by the rules doesn't need to be dealt with individually.
A simpler system could be giving bonuses to generic ability checks (and maybe STs?).
Orcs get +2 to all strength checks and saving throws (not attack rolls, except maybe those relating to shove/being shoved). Elves get a +2 to all dexterity checks and perception checks, and +2 to STs against charmed. Halflings get +2 to all dexterity checks and their nimble traits. Gnomes get a +2 to intelligence checks and +2 on mental STs (again, doesn't add to a wizard's spell bonus/DC) Etc (The "+2" could be modified with "+PB", "expertise", "Advantage" or any other value.)
This way, every race-class combo remains roughly equal in power for attack/spell purposes, but there are still distinct differences.
