You can. If you open the inventory in 3rd person your character will equip and unequip the items in real time. As far as a vanity screen goes, I am not entirely sure that is possible with the current UI and engine. If it was implemented it may cause significant performance issues.
Might be possible if we could jump to 3rd person and change the camera angle on accessing inventory the same way as then crafting. Would not be as neat as in Oblivion but better than current system.