Lots of cost, weight, complexity, and you STILL would have to pick a prop. Too much pitch and the transmission would help get you out of the hole, but your low speed handling and efficiency would suck. Too little pitch, and your drag losses from swinging a prop around very quickly would kill any gains.
A better solution, which is used on large boats/ships, is a adjustable pitch prop. There USED to be a system for small boats many years ago, never really caught on as it really didn't offer any benefit. Ported props are already automatic transmissions for a boat, and it costs next to nothing to drill a couple holes.