Crap, a private hospital doesn't discharge you until you can manage and someone comes to pick you up. And, if you can't manage, they discharge you to a nursing home.
Privatization of government functions should be avoided in my opinion. But we cannot keep having people die while the VA gets its act together. Go to a hybrid system. You call the VA. If they can't take you, they HAVE to find a private hospital or appropriate doctor who will. And it has to be on the same terms as the VA service, with government picking up the cost.
Meanwhile, you're getting the VA to where it needs to be, with a separate team. Also, stop putting military people in charge of the VA. That's not expertise to run a hospital system. That's expertise to be a patient in a VA hospital. Put a professional hospital administrator in charge of the VA and another in charge of the VA improvement team.
Money. If we have the unimaginable amounts to put our troops in harm's way and keep there "for the duration" and to build Green Zones and bridges and keep rebuilding them when they get blown up we have the money to treat the people we put in harm's way.
This is also frustrating because it reinforces the idea that government cannot do anything. We withhold funding from federal entities--certain ones, anyway--and they we say, "They're incompetent. Privatize."