I think quite a few people store their perfumes in boxes and take them out to use them.
I feel a little twinge when I dispose of the packaging but I don't want to keep it. Some parfums and minis stay in their packaging as they are easier to find that way. I find I wear a fragrance less when wearing it requires removing the packaging though. Other things are easier to grab and spray.
If you think you might want to sell some of your fragrances later you might want to keep the boxes though as some people would rather purchase them that way. You could always flatten the boxes them and keep them in a larger box.