I think it sounds like a fun idea but personally we wouldn't be able to do it here because of the "creatures" that are always hanging around the house. I don't think I'd like mice, flea-bitten rabbits, and squirrels making themselves at home inside my house. (Not to mention anything that might show up from the woods nearby.) We did have a mesh "kitty walk" in the past but that was always used when we were traveling and we never set it up outside here.
We used to put the screens down, too... it was right by the soft perch my husband made for the cat. She loves watching squirrels and birds from that window. Anyhow, we always had the window open with the screen down until the late-night my hubby saw a deer come right up to the screen and sit nose to nose with the cat. It didn't scare her or anything, but it made me remember that there have been bear sightings in my area and I really don't think a bear would just sniff at the screen with the cat on the other side and be as "tame" as that deer was... so now windows are closed during the night.