This is still a small portion of overall road damage, but it matters in places like NYC. In particular it matters on our bridges and cantilevered highways, where passenger traffic can't be easily filtered away from weight-sensitive areas like commercial traffic can.
I don't think there would be much point. At the end of the day we'd all pay it because we all consume the goods they deliver or transport during intermediary steps in the supply chain.
I guess you could argue that the status quo is somewhat of a tax incentive that favors local manufacturing (i.e they use the roads for every step of the chain vs imported goods which only use it for delivery). I don't take much issue with that.
Should the rate be higher? Perhaps. But it's already a bit slanted towards vehicle weight based on fuel type and consumption.
Electric vehicles, and especially electric shipping trucks, are going to require finding new taxation sources.
Then the space taken up by unnecessarily big roads and parking lots further stretches distances between destinations out, leading to... more roads required.
I agree with pretty much everything else you wrote, but this it needs to be noted that most road damage is done by weather and heavyweight vehicles like semis/trash/buses/delivery vehicles etc., not regular passenger vehicles.
Semis et al. definitely do not pay taxes proportionate with the damage they cause to the roads, but then again we all need them even if we don't drive.