The same is true of "species". Last I checked, there were at least 24 different definitions of "species", all of which have some overlap and none of which are perfectly precise. You don't see people going around saying "species is a social construct". Then again, maybe they will soon, I suppose anything is possible these days.
That said, you are correct that "race" is merely a rough statistical correlation for some cohort, not some precise measure. If we can categorize more precisely, then we should, and we only fall back to "race" as a last resort (if it's applicable).