A few of us DO use electric trolling motors. After hassling with a 4 hp evinrude for a few years decided to try an old trolling motor I had in the shop... and stayed with it. It's easier to handle than the gasser and it's external tank; isn't near as messy or smelly, it's quiet, and I charge the battery by simply plugging it into the boat's electrical system. It always STARTS, too! The admiral likes it because she doesn't have to crank it.
Downside to electric is limited range and speed; mine is good for 6 mi or so, and it's about half the speed of the 4 hp.
For short trips of 100 yards or so to the beach and back, I use the famous "Armstrong" motor.
For serious gunkholing, or kids, you'd probably want a gasser.