I have a rather different hypothesis in my mind: changing the speed limit does not change the speed of cars relative to the speed limit. People who go 10% over will continue to go 10% over, people who go 20% over will continue to go 20% over. Obviously this can't hold true for extreme values (changing from 50 to 5 or to 500), but in the range where speed limits actually do change from time to time, this is exactly what I see happening.

"Authorities consider this road safe for average drivers at x mph, therefore it must be safe for me at x * 1.y".

The y in the "1.y" pseudomath btw is proof enough to me that claims about enforcement not working are wrong: when you cross state borders it is easy to witness considerable changes in "typical y", the amount of relative speeding customary in the local population of drivers. Road design certainly has an influence on actual speed, but so do limits and enforcement.