No, it does no such thing. Because there isn't one single "Medicare for All" proposal. There are a variety of plans proposed under that title, and only some would do away with private insurance. Many are some flavor of opt-in, granting access to the ability to buy into Medicare in the same way current Medicare recipients choose their level of coverage and pay accordingly, while leaving private insurance intact.
M4A gives everyone, rich or poor, the same base standard of coverage. And if you want coverage for other things that aren’t included under Medicare then you can get supplemental private insurance for it. That’s absolutely not outlawed.
If that's the case then they really screwed up with the term "single payer", and a lot of Bernie's own supporters were wrong. Lot of crap all over reddit about ending private insurance for the last year.