I think the solution to weapons (since every class can't have them for whatever reason, Lore LOL), is to make weapon removal more prevalent. Just forcing every deck to include Ooze isn't really enough as Ooze by itself isn't good in most situations when you'd rather play a class card with better stats or a that actually does something toward your win condition. If the classes without weapons had more access to weapon removal that was PROACTIVE (for instance break a weapon and prevent equipping a weapon for a turn, or equip a really crappy weapon for your opponent automatically, or more ways to freeze opponents) it would be much more fair. Of course, then you might run into a world where Freeze Mage is insane and that isn't any better.
As it stands, weapon classes get a bunch of charge damage that is currently more efficient than the nuke spells that the other classes get. I don't know the solution, but I do know that losing to OTK decks sucks MORE than what we have now. So I'm OK with the current state vs that. Unless Hearthstone allows more interactivity between opponents and across turns, there isn't really a great soltuion to burst damage being good in this game. It will always be good.