Assuming that the goal is healthcare coverage for all: if you have a public system you don't need individual mandate. And you can allow insurers to underwrite, because if they refuse coverage there's still the public system.

With no public system, if you want universal cover you can't allow insurers to discriminate because of prior conditions, risk etc. Or they will, just as they do now.

If you prevent insurers discriminating and require them to offer equivalent terms to all-comers, there's no point being insured until you actually get sick, at which point you can turn up at the insurer's door demanding that they pay your bills. The insurers will exit the scene or go broke.

So without a public scheme you need compulsion for the insurers but also for the consumers. You need to keep as many healthy people in the pool as possible to keep costs down and so that it's a business for the insurers.

If people think of this as a personal rights/freedom issue and really don't want to insure, they can pay the fine. And when the time comes, perhaps they will be glad of assistance from some sort of public scheme into which effectively they have been paying. ;-)