Of course they're worried about criminals and terrorists, as well as protests; nobody wants to watch their children die in a home invasion or a burning skyscraper, not even politicians, and nobody wants habitual violent criminals to repeatedly victimize innocent people (unless they identify strongly with the criminals). Peaceful protests can be a powerful instrument for change, including taking away government power, but only when the protestors are willing to die for their cause.

Every day, police officers and prosecutors go to work and spend much of the day worrying about criminals, and a few of them are assigned to worry about terrorists too. When they go home, they have to keep worrying about criminals, too, because their job makes them tempting targets for revenge. I'm not saying people don't seek employment as police officers and prosecutors in order to have free reign for their sadistic urges --- they do --- but that's not the majority and it's never the whole story.

Terrorism can have extremely large effects, just not desirable ones. When the people think the government is doing a bad enough job of protecting them from criminals, terrorists, and protests, that government is at high risk of losing its power entirely, which is something almost nobody in the government wants.

Even anarchists often don't want it, because there's no guarantee that what replaces the government will be better. You may not like the FBI, but if the alternative is the Proud Boys, better the devil you know. Remember who won the elections after the overthrows of Mubarak, the Shah, and the Tsar.