Imagine that the federal government simply gave all of the VA hospitals to the states they’re in. Instead of the VA budget, Congress just cut checks to states to spend on their veterans. You’d still have problems, of course. But what you would also have are local elected officials — city councilmen, state legislators, mayors, governors, etc. — whom voters could hold directly accountable. Moreover, these officials would be more likely to understand the nature of the problems faced by their constituents.
As a result, you would see states handling similar problems in different ways. Some techniques would be better, some would be worse, and some would just be different. Arizona is simply different than Vermont, so it may handle things differently. Still, this process would allow everyone to learn from both mistakes and successes in a way that a centralized bureaucracy cannot or will not.
Personally, I’d rather see the money spent on veterans go straight to the veterans themselves, in the form of cash payments or vouchers to be used for health care in the private sector. But my point really isn’t to figure out the best way to provide for veterans; it’s to highlight the best way to organize a free society.