In fact, transmogrification has only made the issue worse -- and it all has to do with quest rewards. See, once you complete a quest and get the reward for it, you can't get that reward back again if you delete it to make room for things. Unfortunately, a lot of the nicest sets out there are floating about in 1-to-60 zones as part of quest chains that you cannot redo if you happen to lose that quest item. So if you want to continue to use it for transmogrification, you have to keep it. Forever.
You see the inherent problem here?