EVANSVILLE, Ind.—With engines designed to putter along under 25 miles an hour, it's hard to imagine low-powered scooters as much of a menace to society. But as their numbers have multiplied in this Farm Belt river city, they have sparked an increasingly heated political and cultural fight.

"It's like someone had taken Miracle-Gro and all of a sudden there are scooters everywhere," said Mayor Lloyd Winnecke. "If you spent any time driving the streets of Evansville, you might be inclined to think they have no...