I had a steering damper on a drag bike and one on a 87 ramcharger for the front end that had 33" tires in the past.
I've seen them on big-tired pickups. I think that mud stuck inside the wheel might be the reason for those. That can throw the balance off quite a bit. Even snow wedged and frozen into the backside of a car's wheel will make shake and shimmy.
For trucks I also have a tire lathe, after trueing a tire it rarely needs any kind of balance.
McFarlane Aviation has a video of truing a nosewheel, on the airplane, using a belt sander. But that doesn't address dynamic imbalance.
Most aircraft tires aren't as accurately made as even cheaper auto tires are. Runout is very common. They are also bias-ply, and I think old manufacturing methods are still in use 50 years after the auto industry went to radials. Goodyear often uses heavy balance patches inside their tires, but those tires cost considerably more than the economy stuff. Tubes are also still in use, and they aren't that accurately molded, either.
My evidence is anecdotal. I was the director of maintenance in a flight school, looking after 7 airplanes and sometimes 8. The Cessna singles were bad for nosewheel shimmy and I used to replace torque link bushings and spacers and bolts. I took the whole oleo apart to rebuild and re-shim the steering collar to remove the rocking that results from shimmy wear and introduces slop. I re-rigged the nosewheel/rudder control system exactly as per the manual. I rebuilt the shimmy dampeners repeatedly, with new seals and whatever else needed to reduce any slop. It was all to no avail. It wasn't until I dynamically balanced those nosewheels that the shimmy was finally conquered. Many times the balance was all I did, and it stopped the shimmy.
That shimmy is destructive. It not only beats up the steering stuff, it can loosen the oleo mountings on the firewall, it wears the rudder bars and pedals and transmits violent vibrations down the cables to the rudder, it damages gyros and radios, and so on. Tolerating it is very short-sighted.
Tailwheel shimmy can break that airplane. This is the tail of one of our Citabrias:
See the wrinkling of the fabric just above the tailwheel spring mounting on the fuselage? Note, too, the angle of the tailspring, and the torquing of the lower fuselage members as shimmy racks that tailwheel from side to side. This is what happens:
Broken fuselage tailpost, just above the welded fitting that clamps the tailspring to the aft fuselage. This gets expensive, and it's because students and instructors wouldn't let me know it was shimmying. The shimmy was easily corrected with dynamic balance and a new tailspring to restore the correct tailwheel steering axis alignment.