Eliminating private insurance is fine but I guess I assumed we would...drive it slowly out of business by offering a better product for cheaper, which theoretically is what public healthcare is supposed to be. Are we suddenly now concerned that a Medicare plan with no cost-sharing would fail in the market and needs its competitors to be banned from participating so that it can succeed?
The idea is that by forcing everyone into one plan, you have maximum leverage to negotiate prices with hospitals and drive costs down. Also the egalitarian idea of forcing rich and poor into the same plan, rather than allowing the rich to operate in a high-cost, high-quality parallel system.
That said, whenever Dems take back control, centrists in the caucus probably negotiate this down to allowing anyone to buy into Medicare as a public option on the Obamacare exchanges, allowing employers to buy in as well, dropping the dental/vision included in Bernie's plan, plus more generous subsidies to make sure anyone can buy in instead trying to push the poorest into Medicaid which states can sabotage as we've seen, and harsher individual mandate penalties to make sure young people aren't opting out of insurance and just eating the penalty. That would get you most of the way to the situation you're describing, although with a private market probably still existing for the wealthiest 10 or 20 percent, and for supplemental plans (which would still exist under Bernie's plan).
Especially given that this plan has no funding mechanism, given that they don't have one they feel comfortable selling people on yet, a lot of this probably gets negotiated away, even in a Democratic government, over the course of figuring out how to fund it.
It's not clear to me that this "outlaws" private insurance. See line 8 here:
It outlaws general plans. Private insurance would only be able to offer plans that cover things the Medicare doesn't, which is obviously a much, much smaller market than currently exists. Private insurance companies would still exist, but several would go out of business and any that would remain would see serious downsizing.