I have a couple of doors that stick in an old home. They stick even worse when occupants hang coat racks or mirrors over the door. The doors, like the home, are old and have plenty of character, i.e. wooden, imperfect appearance. Hinges seem good, and the sticking appears to be a combo of doors swelling and of frames being not-exactly-square due to settling, along with the tight fit being tighter in those sticky spots when something is hung over the door. So, I sanded a door down on its top edge (<1mm) using a rasp and sand paper, and it works. The sanded wood looks fresher and has a lighter tone than the rest of the wood door.
The usual next step, I understand, is to apply a thin coat of finishing paint on wood I sanded. Why, if at all, is this necessary? Since the doors are inside the house, protection from weathering doesn't seem like it would be an issue, and because the doors already have an aged woody look to them, these small sanded spots on the edges aren't an aesthetic problem. Is there any need for finishing paint on interior wood aside for aesthetics?