It serves former military but it isn't military.
I still wonder why the VA isn’t part of DoD?
The actual promotion of Veterans Affairs to a cabinet-level department in 1989 was in fact driven by the perceived need to ensure that more attention was paid to the government agencies that administered benefits that at the time covered a third of all Americans. Of course, whether that works or not depends a lot on Congress's willingness to adequately fund the department and the President's willingness to prioritize the VA over any of the many other priorities they must balance.
Recruitment of docs at the VA isn't funded like recruitment in private practice, so they can't advertise as widely and can't pay for prospectives doctors' lunches (much less whiskey tastings). Credentialing now takes six months, due to the previously-mentioned high profile hirings of people without credentials. There's reasonably high satisfaction among docs actually at the high-performing VAs, but people tend to work there because they believe in the mission or don't want to deal with insurance company rationing of care, not because they want to earn lots of money.
source: family member is VA doc attempting to hire more docs to the VA. If you know internal medicine doctors who are looking for a place where evidence-based care is prioritized and insurance status isn't a factor, tell them to apply to their local VA or one of the high-performing ones they might want to move to! (https://www.va.gov/qualityofcare/measure-up/End_of_Year_Hosp...)