Self-paid insurance plans only work if you require every one to buy a plan. Otherwise many healthy people choose to go uncovered and the insurance pools get a higher portion of sick folks. Obamacare tried to get around this by using the individual mandate penalty. However, that was taken apart by the republican congress, so I think it's safe to say that self-pay insurance was/is not straight forward.

The most straightforward way is to have a universal coverage provided by the government (funded by tax revenue). Then we get rid of the whole problem of some people skipping out on coverage and free riding on the system.