I really hate it when people response to single payer with "I don't trust the Government to..."
First, Medicare/Medicate are contracted out to all the same health care companies that currently do employer insurance. They're given tighter money constraints and can't waste as much.
A singler payer would mean contracting out. Private companies wouldn't go away, they'd become government contractors, would need to reduce waste, stop useless advertising and probably layoff a ton of useless people.
I agree though, we desperately need fully universal healthcare .. where everyone gets the exact same level of care because they're a citizen or tax paying legal permanent-resident.