It's a good essay (well-argued, though I don't agree with the strength of how things are stated, but that's a subtle point that we needn't bother with). But this line seems a little glum, or at least unsupported within the essay or with references.
The hope, I thought, of the liberal effort to focus on individuality and ignore race was that in time people would stop paying much attention to race as important, leaving lingering biases to fade away and eventually achieve a fully equitable society.
That didn't pan out as quickly as people had hoped, but it's not clear to me that it wasn't "working", albeit extremely slowly and not always consistently. Maybe the systemic problems we've identified would always remain too great for it to ever work. Regardless, whether or not it was working, I don't think one can just assume that it never will once we address a bunch of the systemic problems.
In order to think that race will always play a major role, one would have to think that race will always be a very important aspect of one's identity. But why should it? Maybe we'll identify more strongly with our political affiliation (actually we already do!), or with our state (in the U.S.), or schooling, or profession, or hobbies, or whatever else, to the point where it's really irrelevant. And because there aren't large majorities in any of those things, the impact will likely be less pernicious and pervasive.
There would, then, still be biases, but you'd be biased towards the Republican in Colorado who studied at Texas A&M and likes long-distance running...and who cares what his or her race is?!