I read this thread as a gripe twixt player/GM-
I love multiclassing. I love unplanned multiclassing. It works best when the player can justify the multiclass within the scope of his character's backstory.
Multiclassing weakens the core concept of a character, you can't glean supreme X if you choose a level or 3 of Y etc etc.
When you take a level 1 of another class, you gain all that class's stuff, this should be canon stuff by now and Desna guide the GM who cannot connect dots.
A barbarian wizard? Well, in PF barbarians aren't illiterate, first, and second, if Uncle Elrond's spellbook is Barbarian's possession, who's to say he can't follow in Uncle Elrond's steps?
Multiclassing wizard in this case draws levels from Barbarian, and whoa, magic missile, burning hands. Plus smash, you go Barb-Wiz.
Games are more awesome when we GMs let players touch the third rail, let them explore their character's potential rather than harangue their creative efforts.
If it makes sense, or at least passes a logical test, why not? (Same goes for Uncle Elrond's pistol.)