Heh. This is one of the elephants in the room that no liberal ever has the fortitude to address.

I'll address it. You absolutely would be able to see every doctor you see now with an actual "Medicare for All" plan. Once all health insurance is effectively nationalized and already pay for, there's virtually no economically viable way for a medical provider to stand outside the system. That's how single-payer systems work - they essentially create a government monopsony, and then providers can no longer play insurance companies against each other.

The other one is if government is paying for your health care they also will start heavily regulating what foods you can eat and how much exercise you have to have.

Seems exceedingly unlikely. They don't do that for Medicare. They don't even do that for Medicaid, where the target population is far less politically powerful/influential than the general population. Such measures would generally be really unpopular - which is why you want to use them as a Parade of Horribles - and so are incredibly unlikely to be implemented. A government that can't even ban smoking isn't one that's likely to be able to "heavily regulate" what people eat. Heck, even though a huge part of the President's coalition is MAHA, they can't even find their way to passing any new healthy food measures, because they keep getting tripped up by industry.

Government doesn't need to be the single-payer provider to regulate what foods you can eat and what exercise you have to have, and a few states have tried very small efforts in that regard. But the fact that those efforts have been very limited shows how much of an uphill lift this is even for jurisdictions that are prone to more paternalistic regulation - you're just not going to see it on the national level.