There are those who claim that storing shoes in boxes is harmful although I have yet to perceive any ill effects. After wearing a pair of shoes, I like to let them air out at least overnight (with trees in place, of course) before returning them to their box. The only time I use bags is for travel.
Shoes just get dirty collecting dust if uncovered. One more stressor on the leather. I'm thinking about putting some of my shoes in a storage box under the bed, (in bags), since I am running out of room in the closet.