It is very relevant as the US system has been working for 100 years or so. EASA has been around a few years but, for light aviation, doesn't work.
Another point would be that the FAA system applies to all FAA registered aircraft, including all those operating outside the US. Moving house is not required
I think a basic reason for the difference in law is that the US has an ownership based aviation culture. Some people certainly rent, but it is considered a stepping stone to a greater expectation of aircraft sole ownership. People tend to take take better care of their own property, and moreover they expect to be left alone to do it. That's just my generalized observation and point of view though.