I concede the healthcare market is definitely subject to asymmetric information which leads to self selection bias (more appropriately called adverse selection) where a disproportionate share of unhealthy seek health insurance and therefore insurers must expend a lot of resources to conduct costly screening thereby raising the cost for all to get insurance and leading to inefficiently low allocations of health insurance.
The solution of mandating all to get insurance can decrease the per capita insurance screening expenditures, but by itself is not efficiency improving. Some people may have individually chosen not to get insurance even at the lower prices induced by the mandate, and so to be truly efficiency improving the policy should include compensation for being forced to take an a policy they didn't want. But, how should the government identify and compensate those individuals. Even the insurance companies that screen for as a profession couldn't cheaply identify those who didn't really need insurance. this is an infringement on liberty for those individuals.
Alternatively, there are non-governmental solutions to asymmetric information market failures (just like Coasian bargaining can be to externalities). Here's the idea. The solution is for both parties to contribute toward improved/additional screening and toward improvements and R&D in screening (medical assessment) technologies. if you are someone who wants insurance and isn't trying to currently mask risky conditions you should be willing to contribute toward this, as should the insurance provider if they see you are willing to.
To me the biggest existing problem in the current insurance market is the monopsony power of the health insurance provider. they have a strong lobby and have earned a political exemption from anti-trust legislation. removing that will increase competition and increase amount of people who can get coverage.
In conclusion, there is currently a market failure, but the mandate is not the most minimally intervening way to do this. A more choice preserving solution that is still redistributive would be to give poor money for healthcare, but require it to go towards the costly healthcare screening via a voucher type stipulation. This new money flowing toward screening should improve screening and generate innovation in that industry thereby could possibly eventually diminish the information asymmetry.