Many bike shops use hooks and hang bikes upside down from one or both of the wheels. I have two bikes and hang one (aluminum frame) on the wall upright, with a hook that holds the top tube. My other bike (carbon frame) just gets leaned up against the wall below it. I also have a set of hooks in my basement and sometimes hang the aluminum bike by both wheels from those.
I've read on the internet that hanging carbon fiber bikes from the frame is a bad idea, so I've avoided doing this... but I also see people (and some shops) do this all the time so who knows? I've also read on the internet that hanging bikes with hydro brakes upside down cause issues with brake lines losing fluid (or something like that). My instinct is that hanging a bike by the front wheel only might cause issues with the headset, so if I were to one-wheel-hang a bike I'd probably do it by the rear wheel.
My guess is that the only potential damage here is from the actual hooks scratching or scuffing the finish of the wheels or frame. Rubber coatings should solve this.