Medicaid is state run. Some states let private insurance companies run it, some run it themselves. The argument for medicaid for all should also be to bring it all together like medicare.
If you want Medicare for all you're going to have barely covering anything for all, and still being mind-numbingly complex.
Other countries have managed to do tear systems, the US kit as well if there were the will
What I've constantly heard from her is that the standard benefits are enough to cover everything but the private addons advertise they can make it cheaper. But as soon as you sign up, Medicare stops covering parts that private addons do (because the private insurance is now getting money from Medicare). This forces a lock in where you can't really go back.
Also from conferences she has attended, there are experts in the field predicting these private insurances are going to bleed Medicare dry from increased costs. What's happening is they keep adding these benefits that only some of their customers use (like silver sneakers membership?) then telling Medicare their operating costs have gone up and they need more money.
If that's the case, then you've never looked into the complexity of Medicare.
Medicaid for all, and concierge services for those who want to pay exalted prices for exalted services -- that may make sense.