Do they? They get moderately annoyed, certainly, and they have every right to. But the DMV issues mistaken suspensions all the time, and I don't think many people see that as either a critically important issue or proof that the government is evil.

I think people do, the idea of being stuck in a bad situation due to a heartless bureaucracy with no way out is something people obsess over, and are disturbed by it happening to even a single person. Have you ever seen "Brazil"? Read something by Kafka? Talked to a (US-style) libertarian or conservative, particularly about the early Soviet Union?