Then we slap a random-ass speed limit sign down and say “job’s done.”

we don't actually--the basis we derive most speed limits from is actually much worse, if you can believe that. from Killed by a Traffic Engineer:

Traffic engineers use what we call the 85th percentile speed. The 85th percentile speed is whatever speed 85 percent of drivers are traveling slower than. If we have 100 drivers on the road and rank them in order from fastest to slowest, the 15th fastest driver would give us our 85th percentile speed.

Traffic engineers will then look 5 mph faster and 5 mph slower to see what percentage of drivers fall into different 10 mph ranges. According to David Solomon and his curves, the magnitude of the speed range doesn’t matter as long as we get as many drivers as possible into that 10 mph range.

and, as applied to the example of the Legacy Parkway, to show how this invariably spirals out of control:

North of Salt Lake City, the Legacy Parkway parallels Interstate 15 up to the Wasatch Weave interchange where these highways come together. It’s a four-lane, controlled-access highway with a wide, grassy median and more than its fair share of safety problems.

So how did the Utah Department of Transportation (UDOT) respond?

It increased the speed limit from 55 mph to 65 mph. It said the speed limit jump will “eliminate the safety risk” on the Legacy Parkway.

UDOT conducted speed studies up and down the Legacy Parkway. It found that most drivers were going much faster than the 55 mph speed limit. Channeling the ghost of traffic engineers past, the safety director for UDOT said, “We decided to raise the speed limit to a speed that is closer to what drivers are actually driving. In doing so, we hope to eliminate the safety risk of speed discrepancy, which can happen when you have a significant difference between the speed most drivers are actually traveling and those who are driving the posted speed limit.”

In the case of the Legacy Parkway, the 85th percentile speeds ranged from 65 mph to 75 mph. Based on that and what it deems engineering judgment, UDOT originally proposed raising the speed limit to 70 mph. After community pushback, it settled for 65 mph.

According to the Manual on Uniform Traffic Control Devices (MUTCD), this slight adjustment is acceptable. The MUTCD specifies that speed limits “should be within 5 mph of the 85th percentile speed of free-flowing traffic.”