Why should the gov be responsible for any of it?
In a more libertarian society the loaners of last resort would be churches, humanitarian organizations, doctors or hospitals providing pro bono aide, etc.
However, I believe that my proposal is a good first step allowing us to wean ourselves from both government programs and the nonsensical notion of insuring peoples' health.
In the future it will be possible that a thorough examination of a person (including a genetic screening) will give an insurance company a fairly accurate estimate of how much care that person will need over his/her life. If everyone is on his/her own then insurance makes no sense. Something like an annuity or HSA would make more sense where the person would put money in an investment fund that they could draw from when they need to pay for medical expenses.
If people are allowed to form groups for insurance purposes then you are naive if you think that the government won't want to get involved in terms of what types of groups can be created, who can be admitted or denied entry into particular groups, and what type of coverage people in a particular group have to support.
If each person pays for his/her own care then there is no need to worry about these grouping issues.
If we were to cancel Medicare and Obamacare and Medicaid tomorrow and tell everyone "You're on your own" that would instigate a major revolution which would most likely end up with us having a British style system or a single payer system like Canada.
These are all less desirable outcomes IMHO.