" It's indeed a social construction, meaning we can change it (well, in this context)."
Social constructions can't be changed that easily. The social construction of race has a long history, and at least in the USA, is a very salient source of identity, and in the case of descendants of the slave trade, the only source of identity that hasn't been completely erased. It's not going to be given up any time soon, as the community around which it is based has almost taken the form of nationality - i.e. black nationalism.
I encourage you if you're interested to read Negro Liberation by Harry Haywood. He explained this very well, much better than I.
"What I'm talking about is that if you want to judge race by colour, what are you going to call (native) Africans who are more white than me? Black?"
No, because they're not black, and they do not have the same history as black people of any origin.