System could be set up which is not part from the government. It has to have element of solidarity, this doesn't inherently come from it being the government: sicker people are subsidized by healthier individuals. Every body pays into this system and it can be separate from government taxes. This could be a solid finance base on top of which one can impose voluntary insurance for extra benefits -- getting better room, color TV, etc. while in hospital.
If it is separate is could be better managed. And there could be more focused pressure on eliminating waste and demanding better prices from hospitals and other providers. I feel it will be less so if money come from the general pool of collected taxes. It will also be more cleanly delineated on your pay check as a separate item.
Modeling paged and segmented memories is tricky business. -- P.J. Denning