Mosca, they've actually tried that! It was made of rock and had like infinite sustain, but was so heavy that no one could hold it long enough to play it (no kidding).

Denser (thereby heavier) wood doesn't damp as easily as less dense wood - something else to consider: the dissipation of sound in water as compared to air. :P

Also, there is a tonal difference. Maybe not just in the weight factor (obviously different woods, cuts, etc have different characteristics), but I can tell you that the same electronics in an inexpensive guitar with lighter wood and another with good heavy wood have their respective quality. I have compared for myself.

The "it's all electronics, wood doesn't matter" argument doesn't take all of the physics into consideration. Okay, you say, it's all electronics - steel strings, magnetic pickups, electrical current - how's the wood effect that. Well, the vibrating strings are attached to the bridge, nut/fretboard, and tuning machines, which in turn are attached to the body, neck, and headstock, which in turn vibrate the bridge, nut/fretboard, and tuning machines, which in turn vibrate the strings some more (not to mention the actual sound waves vibrating the guitar at the antinodes). Not only does this allow the wood to effect sustain (by feedback and sympathetic vibration), it effects the tone by selectively damping some frequency ranges and amplifying others.

Electric guitars are really complex electro-mechanical systems in the way they produce sound, which is why there is no "perfect guitar" leaving all others at the wayside. Because it's not just electronics.