Sometimes duck hunters and trappers use flat-bottom jon-boats pushed by rigs like this. The Dept of natural resources also have a few for doing census counts, etc. The idea is that the operator is able to watch exactly what is happening with the prop, is able to get significant thrust right up to the point that the boat runs out of draft. Crossing logs, snad bars, mud flats, etc. are all possible without damage to motor because operator is able to lift the prop clear very quickly and easily.
There was a movie about 30 years ago called "Dirt", depicting all sorts of off road racing, hill climbs, observed trials, etc. Whether it is still taking place or not is unknown, but I remember a boat race using these rigs...the boat was little more than a glorified surfboard, and the operator stood in the rear, operating the motor. Actually a pretty tough race, demanding strategy...the winner was the fellow who made it the longest before crashing, which everyone did, spectatcularly.
I can't remember details, but there are suppsedly two companies still making them...both use the engine of customer choice, custom adapted to the driveshaft. One popular engine is the Techumseh 2 -stroke because it adapts easily, and is cheap. Some commercial clearing saws work, but are too expensive to cannibalize for this use. The DNR units use detuned yamaha Kart engines, I believe.