"If you want to argue that tax-supported single-payer systems give you more freedom to quit your job and start a startup, fine, but
nothing currently proposed in the US does that."
I think people have missed this point. It's not as if there's a single-payer proposal working its way through Congress, although I think there ought to be. Health insurance sucks; even people who have it are often reluctant to visit the doctor in case it impacts its future coverage although this may result in a loss of economic productivity. A single-payer system will not deliver the desired results to everyone all of the time, but at least it won't treat people as if past illness were somehow a breach of contract.
Certainly, singe-payer means everyone paying a bit more tax to subsidize the least healthy, and if taxes are high enough the risk-/reward ratio of individual private enterprise becomes uneconomic. But if the required tax increases are modest, the benefits for job mobility and general financial security (vs medically-related bankruptcy) will more than outweigh the cost.
Right now an individual's medical problem all too often becomes a financial and legal problem as well. It seems to me that decisions with legal and financial aspects which must be taken in order to obtain medical treatment are made under duress. I had to have emergency medical attention last year and I really wonder about the enforceability of contracts I signed while puking and under the influence of morphine. And I had a good experience overall (no complications, not huge unexpected bills, quick recovery). Given how Kafkaesque the situation is for a good outcome, I shudder to think what it must be like for someone with a deadly or chronic condition.