That's true, but much of the government support has historically come via education funding. For example, most of the University of California campuses have solid research, but a large portion of their money, which provides the base funding for the infrastructure and salaries, comes from their educational mission: grants from the state educational department tied to the number of students they educate, plus, in recent years (as those grants have fallen) tuition/fees. If we decide that we don't really need to educate people that way anymore, then the University of California system should be much smaller (if it still exists at all), and those researchers are going to have to find somewhere else to research, or leave research and do something else.
If that happened, California could take the money they aren't spending on the UC system anymore, and decide just to fund research directly, setting up a state research institution that isn't a university. Maybe they will; I have no idea.