But they don't, especially on the local and state level. They may fund their favorites but outright socialists and communists can and do run in the Democratic p

But they don't, especially on the local and state level. They may fund their favorites but outright socialists and communists can and do run in the Democratic primaries, to say nothing of progressives and Greens. And if I was in a district that had closed primaries where one party routinely wins, I would definitely register for that party. It doesn't mean anything.