This is way off in the weeds, but veterans care (ie, Walter Reed Hospital) got markedly better when they started issuing private sector healthcare vouchers to the veterans on the long end of the waiting list.
That's such a gross oversimplification of the situation at the VA that it would be disingenuous if thought you were actually familiar with the complexity of the VA.
Active duty members also have socialized medicine and Walter Reed is an active duty hospital. The VA system, on the other hand, is its own completely different agency from DoD with its own cabinet head which has suffered from years of neglect, much of it willful under the Bush administration who wanted to brush the tens of thousands of kids they maimed in Iraq under the rug. People like the President (and me when I was on active duty) get treated at Walter Reed. Veterans get treated at VA hospitals, not Walter Reed. Night and day if you've been in both. I've experienced the care in military hospitals which was quite good and volunteer in VA hospitals which can be OK to horrible, and are an entirely different animal. Conflating the two is....well I'll be nice and just ask, now that you know better, to stop doing it.
I'll point out that our families also had access to military hospitals until they decided to contract that out to the private sector. That private sector move was universally awful. My socialized health care, on the other hand, was quite good most of the time. I was lucky to get my daughter, who was born with a birth defect, into our fully socialized military healthcare system before that change, thank goodness.
Which tells us that there is good and bad private sector health care and good and bad "socialized" health care, nothing more. Most of of the VA issues had a root cause of underfunding and under capacity to meet the increase demand the Bush wars caused. So add capacity to a system that's under capacity and of course it will get better, regardless of how you do it. Again, "socialized" is relevant only to the talking heads on Fox opinion and the like who actually know jack shit about that which they pontificate on.