There are plenty government owned registrars. Heck the gTLD .gov is pretty much a goverment entity. They even have policy regarding FOIA requests: https://home.

There are plenty government owned registrars. Heck the gTLD .gov is pretty much a goverment entity. They even have policy regarding FOIA requests: https://home.dotgov.gov/foia/ https://home.dotgov.gov/foia/ which is they are exempt. However, good luck getting .gov domain. It probably is not happening unless your an actual government entity.