Even better would be using this as an incentive to expand and improve the quality of the much more efficient rail network (or transport over waterways, where available) to improve the entire supply chain. That would require the government to act in the interest of its people, though, so I don't think we'll see the effects of such a programme too soon if it ever makes it.
Every tax-paying citizen is already paying this heavy price! Only instead of the damage inefficient transport causes to our infrastructure being reflected in our everyday expenses, it's hidden from plain sight in taxes.
The only industry I'd expect to see killed by paying for road damage would be package delivery vans. They're driving long distances with comparatively almost no weight at all for the convenience of not needing to go to a centralized store to pick up your stuff. With the way Amazon and friends have their drivers pee in bottles, I don't see why we should subsidize those vans.
[1]: https://www.latimes.com/archives/la-xpm-1999-oct-26-mn-26434...