The lost and found is a place to retrieve specific types of lost items where their repository has disappeared (e.g. when the Grange disappears after the festival or when a quest fails after you've donated some items). It's not a dump that holds every item that you've ever trashed or allowed to disappear.
The new shop is to replace items unique items that you've destroyed.
I guess he could've put all destroyed unique items in lost and found, but then the lost and found would be full of your trash instead of actually lost items.