TwoSix
Everyone's literal second-favorite poster
That's irrelevant. Background is what the character was, not what the character is now. I'm sure we all know people who were relatively small, scrawny children and adolescents who had major growth spurts and ended up being large adults.Giving a half-orc the street urchin background is like giving someone born and raised in the middle of a desert the sailor background. Can you pick it by RAW? Sure. Does it make any sense at all? Nope. Street urchins are small and weak. It's what makes them urchins and not toughs or other street people. I suppose if you wanted to play the half-orc runt of the litter who was small and weak, then sure, I'd be okay with him being an urchin. But the typical half-orc won't be one.
And, like you said, even if you do run the game with class as a concept that exists in the game world, there's nothing that requires a PC to be an exemplar of their race and class. PCs are allowed to break norms. That's why you can have half-orc wizards and tiefling paladins.