yes, but the "left-wing elites" aren't the ones pushing political nihilism. "Government is not the solution to our problem, government is the problem" isn't something the left ever claims.
Anyone father left than "slightly more money for foodstamps" may be heard saying exactly that - with the caveat that they're talking about our government, not the idea of government generally.
Marxist here. Just like any libertarian, we acknowledge the capitalist state as a monopoly on violence, but we also acknowledge the capitalist state exists because capital maintains it. When you understand this, you quickly realize that fighting for something like a national universal healthcare program challenges the capitalist state more than anything libertarians want to do.