My dungeon comment was just if you have leftover points and try to exit you would have one more chance to trade in the points while leaving.
I was thinking about that at one point, but I didn't think it necessary.
The point screen shows you how many points you have and how many chest are there still to be opened:
The point of the system is to make people plan ahead and make some tough decisions on the spot. It's pretty much a risk vs reward system.
Let's say you clear half of the dungeon and you have 10 points. You get into a hard fight and you run out of healing items / ammunition or your mood gets too low. You can leave but you also get punished by wasting those points which I think is fair. Or you can gamble and try to push forward to find another chest so you can get some healing items from it so you can try to clear the dungeon.
Opening the item screen when leaving the dungeon would make them way too rewarding and penalties for not being properly prepared would be pretty much non existent.