The Post Office is only failing because the Congress kneecapped it by forcing it to earmark all the social security payments it'll need to make for decades. They just have a massive pile of money that they can't touch because a right-wing congress wants them to fail.
The VA is better than literally every private healthcare provider, the evidence for that being that people use the VA. In a similar vein, Medicare is miles and miles better and more efficient than every private healthcare provider.
How about we do something crazy and tax people on a progressive scale and then just send them all to a common system that is accountable to every voter.