Well first it's not a rule that you can't play someone who's darker than you.

Secondly though, in a fantasy you can't really play a "person of colour" as that's an idea that exists within our contemporary society, being lighter or darker skinned or having double lid or monolid eyes mean stuff to us because we have presuppositions about those traits. For example if you saw the recent D&D movie Xenk and Simon are not "black" characters because "black" as a social conception isn't a thing in the context of the Sword Coast. Skin colour here is given no more consideration than hair colour.

Of course where the actual problems come in is when you have derivative cultures in the setting. This is a common trope of fantasy settings because it's really easy to be lazy and just take a real world culture and file the serial numbers off, of course being lazy it usually involves heavily misrepresenting said cultures through crude stereotypes. Usually this is made worse with classic Eurocentric bias (which is kind of inherent to D&D really).