YES, not enough inventory slots!
NO, just dismantle/discard what you don't want
We each get 60 slots total (right?), anyone think that's just not enough? Especially as you progress further into the game getting more exotics?
I've already found a way around that all you need to do is create a new character when your vault is full then store the items on that character then if you want to use the you just put them in the vault for your main character!