For what it's worth, the US system under the ACA has many of these (probably in large part because Switzerland has them, as our system is modeled in part on theirs). We don't do strong price controls, but we do mandatory insurance, with mandatory coverage levels, that can't be denied or repriced based on age, and public funding subsidizes a large fraction of the insured.
The difference is that Medicaid is a patchwork of various state systems rather than a no-questions-asked federal subsidy. Some states are hostile to Medicaid (e.g. Kentucky with its work requirements). Furthermore, the entire future of the ACA system is in doubt, because of executive sabotage, legislative attempts at repeal, and judicial overreach. All of that leads to people not being confident that they will be able to get the health insurance they need. That's why the Swiss system can fairly be described as universal health care, while the American system cannot.
I don't know. I'm not sold on single payer either, mind you. The only long-term solution I can really see is for the Republicans to fail at repealing the ACA so many times, and for public opinion to be sufficiently against them, that they basically give up.
