I’m not against 18-wheelers.
I just find it hard to believe that the steel rims would cause more damage than 18 wheelers.
2 metal strips, 2 to 3 inches in width concentrating what about 1500 pounds(750 lbs each side) or so of humans and buggy onto asphalt on a warmish day multiplied by dozens of buggies a day would put ruts into roads. I don’t see where the addition of rubber strips or balloon tires helps the road situation since the diameter and force applied is still the same.(a careful design of wheel and axle housing design and rubber however, could redirect vertical force energy forward aiding the horse and away from the road.)
In addition, by adding rubber, drag is added though a balloon tire type situation might ameliorate shock. A better solution might be to widen the wheels to a width that the horse can still pull (what with the added weight), yet wide enough to spread out the concentrated forces so that the rut cuts to the road are minimized.