We had one at the BWV. Both the 1 bedroom and attached studio (we booked as a 2 bedroom) were HA with the roll in shower.
Our room had plenty of counter space. I don't recall if there were drawers in the bathroom or not, but there was certainly enough counter space for us (so rooms vary, but I've noticed from pictures that rooms vary anyway). There was no cabinet under the sink in the kitchen, so the trash was exposed. No kitchen "bar." I didn't notice the stove or counters or bed being lower (remove the knobs and/or burners with little hands anyway - its amazing how fast my kids learned to move a chair to get themselves into trouble), and I've heard the lightswitches are lower, but didn't notice.
It did take a shower or two to figure out the "trick" to not getting the floor wet (making sure the showerhead isn't pointed at the curtain, and a couple of spare towels on the floor). Being a one bedroom, it had the jacuzzi, so a tub for the kids wasn't an issue. (Though at four and five, both will shower if necessary, we don't bathe them more than twice a week unless they get into something (my son has ecxema), and the pool actually keeps them pretty clean)
Having the choice, I would choose a non-HA room over a HA one, but I wouldn't turn down a HA room. Reserving these rooms for only the mobility impared would be a poor use of resources - rooms going unused cost us all money - and, in order to have enough for a rush of the wheelchair bound, they need to have more than enough for normal traffic - so someone needs to stay in them. We don't spend oodles of time in our room anyway. There are requests I would recommend for the BWVs (like non-smoking, close to the elevators) before I'd worry about HA rooms. I'd prefer a HA room over a view of the dumpster, or a smoking room. If I list requests in order of preference, and stick to two requests, Non-HA wouldn't make my list.
We didn't spend a lot of time in the studio portion (my mother in law was in that room), so I can't speak to the counter space or kitchenette in the studio.