Exactly!Warming up has nothing to do with warming down. A warm up helps besides our lips,our breathing, ears,fingers,and our brains. A warm down does non of these things in reverse. When we finish playing,be it performing or practicing, the best thing for our chops is to take the horn off our face,not to continue playing.
Besides I don't know of any venues where the staff wants musicians hanging around playing long tones etc. after the gig is over,just pack up and leave.