In my experience, it can be confusing as it's airport dependent. At some, the screeners will collect and stack the trays whereas at others they just look on while the trays pile up. Sometimes they'll only clear the trays once the belt has stopped due to too many left on there. I typically remove my trays as it takes a few seconds but do see others often leave them. However, I think it's just people not paying attention, not being intentionally rude.

And I fly out of ATL where in the Pre line everything has to go in a tray so there is always a pile of empty trays at the end where people did not remove and stack.