Not to mention the illusion that there's a secret super-socialist majority that's being suppressed (Instead of people who regularly say they like a policy in the abstract but never want the particulars — or are bound up in culture war allegiances.)

It's that last bit: people care more about their predetermined allegiance than policy.

Best example here is M4A: polls are always like “a huge majority of Americans want single-payer, as long as they can keep their insurance”