Medicare does not require you to be part of any particular plan or to pick a doctor. I am also on medicare. You must have opted in to be part of a "medicare advantage program" or similar medicare add-pn. That is what is limiting you. Just stop being part of those HMO's or PPO's then you can choose your own doctor who accepts medicare, almost all of them do, and you won't have to switch all the time.

I find not being part of a PPO or HMO ( yet on Medicare) very liberating, I don't have to be referred ny anyone, when I wanted to get help for my allergies, I just picked out a local ENT doctor office, make an appointment. When I broke my toe a few months ago, again, I just call one of many local orthopedic specialists and go. No waiting weeks, no referrals.....