In the past, residents who smuggled cars to use as school buses for kids in the winter had to work in secret, like something out of a dystopian Fast & Furious reboot. More famously, one guy ferried his car in and drove it openly, certain the rules weren't for real. The automobile was impounded, the whole thing went to court, and the car wound up parked in a barn until such time as the island lifted the ban. The guy died 50 years later. The ban has since outlived him by 30 years and counting.
The island does have a few golf courses with their own electric carts. But if some golfer is too tired to walk home and tries riding their cart into town, that breaks the law and is the biggest emergency the town will see all year. Chris saw this happen -- police chased the golfers in their own vehicle, an SUV that only appears when someone's grievously injured, or worse, is riding a golf cart through town. The golfers were fined and were outcasts for the rest of their time on Mackinac, and that was for driving through town for only 30 seconds. "If they had stopped and got ice cream," says Chris, "there would have been a mob."
It's taken so seriously that mysterious unclaimed golf carts spark police investigations, and the city council puts out entire committees on golf cart use. The only reason you didn't see this already as a storyline on Parks And Rec is that the people of Pawnee were considered too modern and reasonable for that sort of thing.