I would not pin the blame 100% on the hotel management. They do ask us to call Room Service to have the trays cleared when we are done, and I always make a point to call when I have finished and placed my tray outside my room.
Invaribly, it is gone within the hour and any other tray that is in line-of-sight of my room is picked-up, as well.
However, I do agree seeing the same tray outside a room more then 24 hours later is just...well, not "unacceptable", but it should be. I know Housekeeping is not equipped to handle it, but I do think a "final pass" around midnight should be done on each floor.