If everyone does that the system collapsed, as you're free riding on gas and registration fees that fund road you bike on.
A study by the U.S. General Accounting Office (GAO) determined that the road damage caused by a single 18-wheeler was equivalent to the damage caused by 9,600 cars. ... The study found that essentially, road damage was related to the 4th power of the relative loads. https://www.denenapoints.com/relationship-vehicle-weight-roa...
What you're citing is only the fraction from axle weight, exclusive of other damage impactful including weathering.
But for the current roads we already paid for, the average car is apparently around 4100 lbs whereas the average bicycle weight is 30 lbs, so 30^4/4100^4 means that a bicyclist should be paying around 1/350,000,000 of the cost comparable to the average car driver... so litterally a rounding error down to zero.
If you look at Chernobyl (search "Chernobyl parking lot" https://www.vecteezy.com/photo/3732091-pripyat-ukraine-2021-... ) you'll see even 40 years later with no care paving is actually completely usable.
But wait, it's even worse. Cyclists and drivers are benefactors of 18 wheelers. So the cyclist is the worst of all. He gets same benefit of 18 wheelers bringing him goods while offloading unequal axle damage costs on car drivers taxes. Cyclist is ultimate leech in this equation you present.
As opposed to simply changing the tax code to better reflect road usage and wear and tear?
Car drivers don't pay for the damage that 18-wheelers do to the roads in any different way than bike drivers.
When taxes are approximated as first to second order of weight and damage is fourth, the calculus is lower weight cars are shouldering unequal cost of 18 wheelers vs everyone else including cyclist consumers. Effectively part of this is shouldered of free riding cyclists consumption of 18 wheeler goods.
The worst offender here is cyclists, who eat up road space and then buy goods offloaded from 18 wheeler, massively transferring axle weight portion of damage cost to the poor dude in beat up civic.