https://en.wikipedia.org/wiki/.us
But your point about them being rather longer and difficult to remember stands, and the same for a .gov, which could be shorter and catchier.
However amusingly, .us opened up second-level registrations 24 years ago, which means that any qualifying entity could have their name registered directly under .us, which is obviously recognizable, and also one character shorter, than a .gov registration. However, by that time, I believe that .gov had increased in stature so that registering governmental entities under .gov carried more certainty of conveying official status than anything under .us.
Also sadly, QR Codes and URL shorteners today sort of obviate the need to directly register the shortest possible domain name. I don't know: I was always kind of fond of the .us hierarchy, and I'm just personally sad that it's fading away.