Druid of the Invisible Hand
I think you can differentiate races without class restrictions. You just have to not be worried about complete balance. IMO, a halfling or even a dwarf should never be able to get an 18 strength (max for humans in my games) without magic.
I don't feel like that's enough differentation for my tastes. Nonhuman PCs should still be relatable, and similar to Human PCs, but I feel like it should be different experience-- much the way that different classes offer very different play experiences, which is why I always find myself returning to race-as-class.
Which is a lot less restrictive if there's more than one racial class per race, and/or racial subclasses, and/or nonhumans are allowed to multiclass in some "human" classes.