Most people will say that the type of wood and the shape of wood used in an electric guitar is important to the sound produced.  My question is why?

I mean, think about it.  The only thing producing a sound is the vibration of the strings at a certain high tension.  In acoustic guitars, since that vibration is difficult without amplification, the wood is shaped so that a sound hole is produced, a great hollow inside the main body of the guitar which amplifies and allows the strings to resonate.  However, the only thing picking up sound in an electric is the pick-ups, which connect to the input on the guitar and, via a cord to an amp, produce a sound.  So why does the wood affect that?

Here's where I'm coming from.  Personally, I maintain the opinion that people who buy Gibson guitars are primarily paying for a name.  Due to my experiences with them, the price customers must pay for them, and the exorbitant buy-in for small businesses (which is why Chambers doesn't carry Gibson), I sincerely believe that they are the most overrated guitar on the market today.  In all fairness, however, I'm trying to understand what makes a good guitar good before that opinion sets well with me.

Also, one could say that something's greatness is the sum of the greatness of all its part.  Do you agree that that rings true for guitars?