I use the VA in Minneapolis, we don't have a specific clinic and go to the individual departments for our care. While I can see the benefits for the "one stop shopping" setup, it can also make it more daunting to some to actually get started, with the whole being marked out as going into "that wing" of the hospital.
But once in there, it would make it much more comfortable and less stressful as you wouldn't have that worry of being misgendered or deadnamed and outed because of the system not being able to display perfered name and gender.
So basically, I see benefits and disadvantages to both setups. Meh.