The GVWR on a F350 is around 10-14,000, so somewhere between 5-7k axle load.

Yes that's the gross weight, i.e. carrying its maximum rated load. Personal vehicles are very rarely loaded up to their maximum weight, and mostly are driven relatively empty.

Even driven at gross weight, it's doing 5% of the damage per axle of loaded semi. The semi also has 4-5 axles, so it's more like 2% of the damage of the semi.

Mind you, we're talking here about the most damaging personal vehicle loaded to its maximum weight, and the semi is still doing 50x the damage of the personal vehicle. It's reasonable to say that essentially all road damage is done by semis.

For the most part I agree. The other issue is psi load produced by different tread patterns. Going from some minimal water channels to a mud terrain cleated style will reduce surface area a good bit. If you have experience with rural areas you don't need a calculator to observe the highest direct damage is usually from agricultural tractors. Deformation from a single pass can be observed (and often felt) with the naked eye in many cases.

Well, after all, the whole point of these tires is to dig into the "road" to get better traction than is possible with normal friction, so it's not too surprising that they dig in to a lesser extent on hard surfaced roads.

That said, this type of tire is a very tiny fraction of the total miles driven on public highways, and so if you're looking for someone to tax based on the costs they create, it's all heavy trucks.

Where are you getting your "over 99%" figure?

You need to approach or exceed a roads per-axel weight limit to do any damage or serious wear.

Trucks and permit loads are pretty much the only things that get close.

Beyond the elastic limit, damage is an exponential function of the pavement loading, but only once that certain minimum psf is hit.

For the majority of a highway's loading curve, the damage-per-force is essentially nil. Plastic deformation and serious fatigue only start as you approach the design limits.

It's 99%+ because cars don't do any real wear or damage to pavement from typical use.

A semi is doing 400x as much damage as essentially the heaviest personal vehicle driving. For a more typical car at 4000 lbs (2000 lbs per axle), the semi does 6000x as much damage. If semis are 2% of all traffic (true in my observation), they're doing over 99% of the damage to roads. It makes no sense to care about road damage at all from any vehicle other than a heavy truck.