Ideally, in the so-called “free world”, we should leave the choice of contributing to a collective or private insurance plan to the citizen :

• If an individualist prefers a private insurance, then so be it, s·he won’t have to contribute to the collective ;
• If a socialist wants to pay for the community instead, then s·he should be able to contribute to, a’d benefit from, a public insurance instead.

Apparently, we’re not given this choice mainly because of the adverse selection : private insurances are cheaper when you’re young, while public ones are cheaper when you’re old. This would make people subscribe to private insurances at first, and then switch to public ones later, which would cause the subscription costs of the latter to increase a lot.
That’s why Germany allows the wealthy who took a private insurance to stop contributing to the public one, however they can’t switch back to the public insurance past 55 years old.

If adverse selection is the only reason not to give citizens a choice between public//private insurances, then the solution seems obvious, we only have to ask those who switch back to public insurance to pay for the contributions they missed(, minus the estimated costs that the public system avoided).

In almost every country, citizens are either forced to contribute to the public system of insurances, or there’s no public protection and they’re forced to subscribed to private ones if they can afford to.
I doubt that what i proposed is the solution to offer a freedom to citizens of any country, because it’s so easy that governments would have already thought about it, but i don’t understand what ‘mistake i made’/‘i missed’, perhaps that some people of Lemmygrad could shed some light on this for me ?

Of course, it’d be forbidden not to have an insurance, you’d have to choose between private or public.
Otherwise, in a country without mandatory healthcare, the poor would struggle to get healthcare and, i.m.o., the wages would be reduced to the new minimum in order to maximize profits.

I suppose that the main problem would be that, in their old age, some people would be unable to continue paying for private insurances and also to pay for the missed public contributions. But that’d probably be an exception that wouldn’t weight too much on the budget of a last-resort public coverage ?