If it turned slower, it would drag on the pavement. In order to maintain the same roadspeed as the rest of the vehicle, a smaller tire will turn faster. The increased amount of rolling resistance just means you are using more energy.

I have a problem getting wally world to keep my tires sealed on the rims in the cold and the hub was done about the time it warmed up so couldn't tell till next winter and new tires will get put on in the fall.