It's even more complicated than what you've described. Most modern intelligence tests (WJ-III Cog, WAIS, SB) incorporate WIS (as you've described it, Gc / knowledge) as a component of intelligence. And in actuality that kind of general knowledge has stronger links to general intelligence than just about any other measure on those tests. What it boils down to is that how much you know about the world is a pretty good indicator of intelligence, and by extension, is a pretty good indicator of your _ability_ to thrive.
So yes, IQ is an aggregate measure of lots of diverse qualities, but WIS is definitely one of them. And it happens to be one of the best.
Personally I always liked Heinlein's take on what a man should be able to do... It's very similar to Wechsler's definition of intelligence, only described in example behaviors:
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Heinlein, Time Enough For Love