For example: https://ezbuy.chicityclerk.com/faq-vehicle-sticker
Motorbike $50.52
Vehicle with curb weight of 4,500 lbs or less with a payload capacity of 2,499 lbs or less. $95.42
Vehicle with curb weight of 4,501 lbs or more with a payload capacity of 2,499 lbs or less. $151.55
Vehicle, Truck, pickup truck with ... a gross weight of 16,000 lbs or less or with a payload capacity of 2,500 lbs or more. $224.51
Truck or vehicle with a gross weight of 16,001 lbs or more with a payload capacity of 2,500 lbs or more. $505.16
Interestingly, minivans are most commonly the thing that surprise people. The lower trim levels usually qualify for the $95 annual sticker but the upper trim levels just barely cross the threshold and must pay the $151 annual sticker.[1]: https://www.seattle.gov/transportation/projects-and-programs...
1. Not give an opponent an easy way to attack you that requires the masses to employ nuanced reasoning to understand why that attack is wrong.
2. Say things to your base to keep them voting for you even though you have no intention of implementing those policies.
Edit: The nation as a whole has shifted very much rightward the last 50 years. Instead of saying Republicans I should maybe say “right leaning politics”.
If it was a politics thing and not a "everybody who looks into it with any depth decides it's dumb" thing then some state like MD, RI, CT, or MA would have taxed it already.
Furthermore, we're talking about "damage" (in sarcasm quotes because expected and normal wear isn't damage in any normal sense of the word) power equation here[1]. So basically everything that isn't a class 6/7/8 truck is inconsequential for a road that has any portion of its traffic made up by those vehicles. Since those trucks basically run the economy someone has to pay for it. There's really little political will to engage in an obvious exercise of "picking who to screw" like that vs an imperfect but fairly fair fuel tax.
[1] https://www.insidescience.org/news/how-much-damage-do-heavy-...
EDIT: It is definitely not a dumb idea as you suggest. Many counties have sensible policies on this issue and yet they manage to trudge along without much trouble. As I said it is OK to advocate for pay-as-you-use government so long as people like you don’t pay for your negative externalities too often.