The military is a federal issue, those other programs are not. Look to your state.
Curious, do you think it would be legal for California to go single payer and refuse coverage for anyone who wasn't born in California (or lived there for > 5 years).
Don't worry, Californians aren't progressive enough to try something like that. But for a state-level healthcare program to work, one would have to exclude people from other states. Otherwise, all the people who can't get insurance will move to the given state, and effectively break the program.
IMO, state-level single payer could work just fine. It's how things work in Europe, every country has it's own system (some more privatized than others).