My medicare Advantage plan pays for anything Medicare covers. Medicare decides what it will cover -- your doctor does not. For Medicare to cover, it has to be medically necessary, also. Medicare doesn't just give you a blank check, it decides what it will cover and what it will not. So it acts as your insurance company.
My Advantage plan (for which I pay nothing in addition to the regular Medicare premium) also pays for prescriptions, vision, etc., and several things Medicare does not. The HMO I am in is huge, and most of the doctors here either accept it, or the other major Advantage plan here, or both. My sister and I both had hip surgeries, and we used the same surgeon. She had one Advantage plan, and I had the other. Here, at least, the restrictions on doctors you can choose is not a problem.
As to the out of pocket caps -- I had two hip replacements in 2013, for which I paid a grand total of $100 to the surgeon (for all the visits together, and the surgeries) and about $600 in hospital co-pays (for both surgeries together). I paid nothing to the anesthesiologist, or for diagnostic tests, or home PT, or anything else. And I had no Advantage premiums. My sister had the same scenario, but her payments were a little different (negligible difference) because she was on the other plan.
I saved a heck of a lot of money for two VERY expensive operative procedures and a total of 5 days in the best hospital in the region.
They all work differently.