This is pretty much what happens right now in Australia.
All income taxpayers pay the Medicare levy. A large payment base means there's enough in the nation-wide pool to cover pensioners, unemployed, etc who can't afford to pay-in.
Private health insurers then come in and make a killing on gap insurance and covering things Australian Medicare doesn't - like dental.
1995 called. They want their instant messaging back.
This is why one should always refuse a breathalyzer test even if you haven't been drinking
"Refused to give a sample of breath for analysis." Instant fail. Off to gaol for you. Thanks for coming.
It's a naive, domestic operating system without any breeding, but I think you'll be amused by its presumption.