The VA problem is not new, just getting publicized partly due to the increase in their load (WWII and Korean War vets are aging, and new veterans from the various Gulf wars enter the system).
The real problem is the bureaucratic mindset, that puts following the rules as the most important thing.
I remember going to a conference where a representative from the area office of the IHS told us that the IHS was tasked to supply medical care to the Indian people within the limits of the budget. I interrupted her and pointed out that the IHS was supposed to treat the Native Americans, and that the mandate that started the program didn't mention the word, budget. After correcting her (twice) she ignored me and went on with her program.
If you think the VA is bad, try working with the IHS. And yes, they do budget care for "non essentials".
which is why those suggesting single payer care never bother to point out the success of the IHS or VA as examples of why it would work.