Think about this...if car does 'x' damage to the road, 2 cars does 2x damage. 2 cars welded together side by side (axle to axle so the axle count stays the same) would also do 2x damage, but the 4th power law says it does 16x damage.
If it's wrong by a factor of 8 in the simplest thought experiment it's not a law. You can obviously make a heavy load act like many small ones, or concentrate a light load so it does a lot of damage.
Constant * X^4 just coincidentally went through the data in a single 1950s dataset...and for some reason we're calling it a law 70 years later, when it's really just a loose trend that we could easily break with a little engineering. And we probably have broken it...tires, roads, and vehicles have changed a fair bit in 7 decades.