But what motivates the board to pay the executives so much?

Either the board is corrupt and is wasting company money on their executive buddies and the shareholders ought to discipline the board (and perhaps putting some salt-of-the-earth workers on it may be a good way to do that, but certainly no silver bullet), or they pay what they need to keep the executives from jumping ship and go work for a competitor, and they are in fact not overpaid. I suspect there are companies that fit in either category.