[nfnaaron]

"So what have we really gained here? All we've done is made sure the initial positioning of the coin is random. The bias in the toss itself is still there, but we're hiding it by making sure the caller doesn't know the initial state of the coin."

Assuming the cupped hands shake produces a random starting position, you've evenly distributed the toss bias, so the result of a series of tosses should be evenly distributed.

"If that's the case, then why not: a) Don't even toss the coin at all. If we're convinced that the act of the ref shaking the coin around in his cupped hands gives a random starting position, then why not use that in place of the coin toss?"

That's an excellent simplification, but it just doesn't feel as dramatic and traditional to decide on shaking cupped hands. You need the toss for effect.