The two big (and very real, based on current experience) problems with that approach:
1) Many of the uninsured will avoid preventative care (including medications), and will end up with chronic conditions...
2) ... that being uninsured, they will end up having treated in high-cost settings such as emergence rooms.
Which, as you note, the rest of us end up (cross) subsidizing.
The first problem (preventative care) - I agree. But, insofar as some preventative care is a no-brainer, I would think that in a free society, do-gooders would try to communicate the no-brainer preventative care to less informed people, on a voluntary basis. While extreme libertarians might be o.k. with dog-eat-dog, law of the jungle stuff, true conservatives like do-gooders and see voluntary charity as the solution to many tough problem. Socialists, on the other hand, have no problem with invoking the power of the state.
I should mention a kind of half way measure: the government might require a medical savings account in conjunction with a catastrophic health insurance policy. This way the out-of-pocket issue would be taken off the table.
The second problem is not a social problem. It’s an individual problem. If people have catastrophic health insurance, they will pay through the nose for the deductible part of extraordinary expenses that could have easily be avoided with preventative care (or better lifestyle choices, or whatever). But, isn’t that the problem with self-responsibility? People are not protected from the consequences of their decisions.
If insurance policies are owned by individuals, low-deductible HMO-type plans, high deductible catastrophic plans, and traditional cost-sharing Blue Cross-Blue Shield-type (or traditional Medicare-type) plans would probably all be out there.