The difference between paying $0 and $200/month (especially when the first option is tax-subsidized) is trivial compared to the current situation where any "insurance" individuals are graced with being allowed to purchase can be revoked arbitrarily.
So, please, get your facts straight.
If you think that $200 a month is what mandated insurance will cost a family of 4 who aren't Medicaid-poor, I don't know what to tell you.
Financially-savvy young entrepreneurs with families would obviously be better off with high-deductable plans and HSAs, which cost significantly less than $1200/year. But again, they can't do that, because private health insurance isn't guaranteed-issue.
Mandated insurance with guaranteed-issue is a tax on the young and healthy to subsidize the old and sick. My plan, for example, is illegal in NY and NJ which have strong community rating requirements.
You can certainly think that taxing single 20somethings to subsidize families and the elderly is a good decision as a matter of policy, but it's not going to do a whole lot to increase entrepreneurship.
Without a mandate, how do you provide any reasonable coverage to the unfortunate without falling prey to adverse selection?
This argument just doesn't seem well thought out.
If you make healthy people buy fairly priced catastrophic coverage so that if they have an accident they don't declare bankruptcy and stick the rest of us with the bill, that's not a subsidy. It becomes a subsidy when you force them to pay the same rates as less healthy people, or force them to buy comprehensive policies that go beyond the coverage that they actually need.