I really think people should realize there is a difference between "wetsuit", as in simple 3, 5 or even 7 mil suit, and "wetsuit" for PNW diving, which is a 7 mil suit with a 7 mil corewarmer, or 14 mm of neoprene on the core, and at least at our shop, an attached, integrated hood. It's not easy to flush those suits with water -- they're rather designed to avoid it.
Could a student spend a few minutes in the pool in such an outfit? I would imagine of course. Would it be long enough to make a difference? I don't know. Would it be hard on the gear? After watching my wetsuit booties disintegrate from just the occasional pool sessions I do in them, I would imagine so. Is it expensive for a shop to replace that much neoprene? Yeah.
As much as I think it would do some students good to dive their heavy exposure protection before going to cold water, I do totally respect the reasons the shop chooses not to allow them to do it. I do tell people it's a good idea to put their wetsuit and BC on, with weights in, the night before the OW dives, so that at least the process of getting into it, and how much it all weighs, will not come as an unpleasant surprise the next morning. I don't think many people bother, though.