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