@Qingu Well, nobody has to buy into Medicare. It’s an entitlement, which means you get it (at least Part A) whether you need it or not. Part A covers hospital care; Part B is nominally optional (meaning you can refuse it, but in most cases you would be a fool to do so). It covers all doctor visits, specialists, tests, physical therapy, medical devices and major prescription drugs. It costs about $90 per month (deducted from your Social Security check), otherwise you have the “choice” of paying things like MRIs out of pocket, that can easily run $1,600.
Medical Part D, which covers an expanded drug formulary, is also optional. People who have health insurance as part of their retirement get most of what Part D covers at no cost. This “Medi-gap” insurance pays any difference between what Medicare covers and whatever your former employer would be giving you if you were still employed (which is less and less every year).
So, under Medicare, you still have the flexibility to refuse parts that would be redundant with insurance you already have, but the basic deal everyone gets is the Medicare deal. And it is a pretty good deal. But, if you can get better, nobody is stopping you.
Medicare is single payer insofar as it is your primary insurance. If something isn’t covered by Medicare and you have secondary insurance that covers it, then the secondary insurer pays. You have one, very easy billing system for the whole sheboot, and you don’t have to put up with automatic denials and all the other runaround you have to put up with with private insurers.