Via Austin Frakt, there is an interesting piece on defined contribution health insurance. It is an interesting idea and likely not a bad policy direction. I know I would contribute more to my health saving account if the balance could roll over. But, as things are currently set up, it is impossible to plan against a major medical event.
I think that it might be useful to consider this model with some tweaks. Essential to making it work is to include catastrophic event coverage (major medical insurance). Patients will not go out of their way to have heart attacks, stroke, and major cancers just to take advantage of their health care insurance. These events are what really create the "risk" (and thus insurance) part of health care.
Otherwise, it is actually plausible for people to budget for health care expenses and tax sheltered accounts might be a great transition move.