Just to be clear, you could pick any active any skills from any tree, not just weapons, for that skill bar. The weapons just switch the skill bars. So, yes. 
I noticed there was a mention of armor switching and other factors that would make the deck building have too many options. Or more to the point, there would be too many decks to build to make this option viable. I don't think that is true.
I mean, if you gave every player 10 deck builds per character, I bet that would cover most players needs. You have 6 weapon swaps over all, right? (Two handed, one handed+shield, duel wield, bow, attack staff, healing staff). I bet most characters will not be actively using all 6 sets most of the time. I would think each character would use 2 to 3 at most, for any given time. (not each player, each character) Don't get me wrong, eventually most characters will probably use all weapon sets eventually, but at any given time, they would probably only be working on 2 or 3.