We always used our travel trailer in pretty much the method you describe. We referred to it as "a big long vacation". Didn't sit in any one place very long and moved on wherever we chose when we felt it was time to do so. You MAY find that you want to re-think the "no towed" rule as it can be cumbersome going to the grocery store, out to eat at a nice restaurant or even getting into some of the major attractions with the motorhome as transportation. One possible way around it is to consider renting a car for any place you will be staying for a given period of time. We chose the trailer trailer for just that reason, we can unhitch and have our truck to get around in easily. Lots of different ways to accomplish the same things.
The exception to our "vacation lifestyle" was the winter months. We would take a more traditional view to December, January and February and set still for much of the time but even than we had a kind of route and would divide our time between three or four different locations. Old habits die hard :)
Good luck / Skip