I'm worried about the tragedy of the commons.
There is an appeal to a shared burden, but there needs to be a disincentive from overuse. Perhaps you would limit the number of services, and any extra would have to be paid for by the patient. Maybe some people would get insurance to pay for extra services.
My thinking is to get closer to a free market. Have a tax-deferred medical savings account, which could be used for insurance or medical cost directly. Allow all medical services to advertise prices, which is pretty much banned right now. Have employers contribute 5 to 10% of a person's income with an equal amount coming from the employee. Give employees the option to contribute more to the account if they feel that they need to. Allow the money in the account to be invested. If the account creates an apparent surplus, allow a portion of it to be used as taxable income in retirement. Make the account inheritable, so that it can be passed onto family members.
Such a program would need a subsidy for low-income people.