People do it all the time. Once you've paid for your campsite, it's yours if you are there or not. Every state is different, but in Indiana, there is a 14 day rule. You can stay for 14 days and then you have to leave to come back. I think (if I remember right), it's 3 days and then you can stay another 14 days. Something to think about.
Also, State Parks will range from about $25 - $40 a night, depending upon which state you're in and what type of campsite you get (electric vs primative vs full hook-ups) Even at $25 a night, I...personally would prefer to sleep in my own camper, rather than the floor or the couch of a family member's home any time.
When we visit family in neighboring states, we have THEM come out to the campsite and spend time. They enjoy getting out of their homes and we're not invading their space. Everyone is happy.