Really? Which resorts? This has never been the case in my stays. It would be a peculiar question to ask a guest with luggage in tow if they are staying there. We were at AOA as recently as October, and I stored our luggage after check-out. The handler just took my name and wrote down how many pieces we were storing, handed me the ticket, and we were on our way. Perhaps it varies by staff member if they take your room number or not.
OP - personally, I don't think it would be an issue, especially since some of us have not had them even ask for details. BUT I can't confirm whether its actually permissible, and no one knows if they'd be given a hard time on the day of. Also, PPs raise good points in that they wouldn't be able to bring it on Disney transportation in order to get to the monorail resort, and it likely would take just as much time to drop it off there than it would to just retrieve it from the All Stars at the end of the day. Luggage storage is usually at the front of the resort near the bus stop anyhow, so they should be able to quickly retrieve it from there and then call an Uber (or whatever) to go to their next hotel.