I think auto insurance is a good indicator of how it would play out if you made everyone do individual insurance. Insurance would still likely need to be legally mandated, like auto insurance, so that the insurance market would be solvent.

From there, insurance would likely break down into high cost / high coverage, mid cost / mid coverage, low cost / legally mandated minimum coverage.

The poor would end up with the low cost / minimum coverage plans as cost would likely end up being the main motivating factor. Given that 6-in-10 Americans can not afford an unexpected $500 bill (https://www.cbs19news.com/story/34248451/6-in-10-americans-d...), this would likely be the coverage level chosen by about half of Americans. These policies would be affordable, but I expect the deductibles and co-pays would be high enough to make it prohibitively expensive for policy holders to actually get much utility from them.

The other half would end up with the better plans, unless they were more comfortable with risk and elected for the cheaper plans. Their lot is probably pretty similar to today.