Recently I was asked about medical issues and able to keep our personal doctor of preference. This is a difficult question to answer; however, I'm still working on it!! The wife and I are NOT in one location long enough to establish a lasting relationship with a "family physician" or "practitioner" that we PREFER above others.

FIRST....God is our Physician, and we call on HIM first!! He will not fail us!!
He doesn't have a HUGE waiting list!! His "waiting room....emergency room is NEVER packed full of patients"......

One of the primary difficulties being that we are not always sure of where our next work assignment will be. We do have medical issues that require us to see a doctor on a regular basis. Both of us are diabetic, have high blood pressure, and other issues. Myself, I had open heart surgery with triple bypass, two strokes and three heart attacks within 72 hours prior to the surgery. It is critical that I see a cardiologist every six months. IF i am in the area of one that I have already seen before, I do my best to see them again.
Another issue is that when you move into an area, the one's taking "New Patients" are almost always NOT PHD's but Liscensed Nurse Practitioners or the like. I have nothing against these fine people, but they always have to refer you to a Specialist....in my case, a Cardiologist.
Solution (of sorts) is that we keep on our computer records from previous doctor visits and give the physician or practitioner access to those records. In Oregon, we have the Health Science University system, in AZ they have their own, in WA they have their own.....so having a means for them to access our previous records is our ONLY real answer to having a connection with our preferred physician.
When we return to the Portland, OR area we will re-establish our connection with prior Cardiologist in Vancouver, WA and practitioner in Portland, OR.
Not sure if this helps much, but YES it is an issue! With medical changing as it is, so INCONSISTENT, we are finding not all doctors want to take Medicare patients, and they have LONG waiting lists!! My greatest fear is this new trend "Medicare For All..." YEAH RIGHT!!! I was having a heart attack (so I thought) and the emergency room was unbelievably PACKED!
So I went home, called an ambulance, and found out I had severe pancreatitis!! Once five days in the hospital, and the second time eight days! That may be our only recourse in the future! Who knows!