How can the government serve the people if it can't sustain itself?
If the people present a democratic threat to the government, the government should fade from existence peacefully. If people present a non-democratic threat to the government, then the government should act to protect itself.
Anarchists do not, categorically, present (or seek to present) a non-democratic threat to the democracy.
Do you want to keep tabs on violent* anarchists? Knock yourself out. I have no particular issue with that.