Nah. It's quite easy to ignore how we treat old and sick people, too. So what you're suggesting is we'll end up with a system that sure is good for people who have small illnesses (take an antibiotic, sleep a few days), but the truly sick might have several month delays in getting care.
Not really. There are slightly sick and truly sick, young and old, etc VA members too, so the order of magnitude difference between the VA and a universal single payer system still hold.
The only thing we know for sure is that on a global scale single payer systems perform better. On a dollar for dollar basis the difference is even more drastic, with single payer systems being an order of magnitude better than our system. We have worse health care outcomes than most OECD countries, but spend more than double per capita. We can quibble about why the VA has been mismanaged, but there is no honest debate about whether single payer systems have outperformed our system in nearly every metric (they have).