This couldn’t really be anything better than a cosmetic change, I fear.
The DOD would, in effect, be pulling the Veterans Affairs under its roof. And as pointed out, the management of this “cat-dog” agency would have inherent conflicts. I think Carson sees this as a shrink-government move but hasn’t thought through the management issues. I agree that generals don’t need, or want, the headaches. This is an issue for the civilian side of government to manage.
Generals should be focused on winning wars in my opinion.