We found that we wintered in one state so we established doctors there. Never paid a new patient fee and it was easy to find a good doc.
Dentists - we've gone just across the border to Mexico if we're nearby. Otherwise, it's easy to find one while traveling in an emergency.
We've also used doctors as we've traveled in an emergency - even in Canada where we found an awesome caring one - even called later as we continued our journey to see how I was doing.
With all the new insurance stuff in the past couple years it might not be as easy but don't know. We're on Medicare and have a supplement so no problem for us. I feel sorry for the younger full-timers that have to purchase their insurance with all the new restrictions.