It's really not easy. They more or less have tenure. They can only be fired for cause and they have a right to due process. These are legal rights that normal at-will employees just don't have.
Non-unionized employees don't have, but yes, it's true that they require a fair process. In this thread we're talking about people who are performing badly enough to matter — that sounds like giving someone an unacceptable rating, telling them what they need to do better at, and firing them if they don't improve. The government managers I know who've done that hate the insinuation that it's impossible since that's basically saying they can't do their jobs.