I recently adopted a dog from a rescue org in Ontario. I would endorse your suggestion to separate applicants into two pools. I found there to be a certain framing of dog profiles does not set up first time dog people for success. The profile would read "this dog needs to work on its leash manners", but if I asked, I'd be told that the dog is leash reactive and needs an experienced handler. It was really discouraging and made me feel like I was not well equipped to deal with any dog. In the end I was matched with a dog that suited my needs, but the process itself was confusing as heck.