...Which doesn't guarantee continuity of existence, or the existence of a working government along with the flag.
The fact that Cochrane is building his warp ship out of a still-operational Titan missile at an abandoned USAF silo farm, out in the open, tells me that there isn't much of a U.S. Government left to stop him.
Or then he's working for
the government, as one would generally expect for such a project. It's not that there isn't anybody to stop him - it's that the paychecks are late, the colleagues have moved up in their careers (sustenance farmer being a favorite), and the last report sent to Houston came back stamped "Address unknown/City Not Found".