Many Amish churches ban rubber tires and the buggies will at best use hardwood wheels, and otherwise they’ll be steel. Weight is of some minor concern but more principally the hard materials as well as the shoed horses wear away at the road. In high density Amish areas it’s common to see two deep grooves in the road from buggies.

Buggies are not designed for modern roads. They have very little safety features (in fact they only begrudgingly even put reflectors on them, and maybe occasionally flashers for at night), and their bulky, dense bodies and slow movement make them pretty devastating targets to hit. They don’t crumple like a modern car. They explode. Car-on-buggy accidents are very frequently fatal. I know plenty of Amish who have lost family to accidents at relatively slow speeds.