You are not getting your money back. Your money when you were working paid for Medicare beneficiaries at the time. Similarly, taxpayers now are paying for your Medicare benefits. It is a wealth transfer just like every other social program is.
FDR did not create Medicare. It was signed into law by LBJ. A Medicare Supplement is a supplementary insurance to Medicare that pays for the out of pocket fees that Medicare doesn't pay for. Medicare is just like any other insurance policy in this regard (actually its far more generous than most insurance policies today are). However, because your healthcare utilization is much higher in retirement than it is when you are younger, many beneficiaries carry a supplement to pay for their out of pocket expenses.
Let's say we didn't have Medicare. And you got to keep the 1.4% or so of your salary that went to the Medicare program. So you could invest that, just save it, whatever you wanted. You turn 65, what do you think your health insurance premiums on the private market would be?
At 65, assuming you were fairly healthy, you would be looking at around 25k a year. By the time you were 70, your risk to an insurer would mean your health insurance premiums would be around 35k a year. By age 75, they would be over 50k a year, by age 80, they would easily be over 80k a year due to the extremely high risk you would pose the insurers. A 70 year old to a health insurer is the same kind of risk a guy with 5 DUIs is to an Auto Insurer. Now the only way an insurer could lower your premiums would be if they were allowed to have an annual cap for what they could be out should you get sick.
Are you saying that had the government allowed you to keep your 1.4% of taxes that went into the Medicare program, you could have saved enough money to be totally self sufficient, to pay for your own subsidized health coverage in the private market once you hit retirement?