It is a social construct, but the point of that construct is identity, not a direct exercise of power. Race ('white' race especially) is an "easy" answer to the perceived problem of "what am I supposed to identify as" for many Americans. And renouncing one's self-identity is really, really hard so it's very likely that this social construct will be sticking around for a while, whether we like it or not. Of course, this also implies that whenever we engage in derogatory discourse about "white race", "whiteness" and the privileges thereof, we're launching a direct and sometimes vicious attack on what many millions of people see as part of their deep self-identity - which of course can be seen as rather disrespectful, and liable to generate pushback of some sort!