The fourth power law applies to weight per axle, assuming identical axles/tires. In reality, the typical tandem axle arrangement on big trucks (18 wheels across 5 axles, the four back axles paired together as tandems) spreads the load over a much larger road surface area than a typical 4-wheel passenger vehicle.

Also, the models themselves aren’t that robust. It’s from a single comprehensive study of loaded trucks, from 1958-1960, that has been very influential, but the tests itself never went down to passenger car weight.

Civil engineers have models and formulas for that, and there is indeed much more road deformation from the heavy trucks, but it’s probably closer to thousands of times the load for an 18-wheel tractor trailer than for a passenger vehicle, not 500,000. Note in that analysis, it talks about which power to use (not always 4) for different types of road wear or damage, and many of them are less sensitive or more sensitive to vehicle load.

It’s all interesting stuff, but I worry that people on the internet have put way too much value on the fourth power law here, stretching it beyond the original scope or overstating its applicability to practical road design issues.