Here's some support from a different direction.
Starting a couple of years ago, Virginia started bumping up the speed limit on the more rural sections of interstates from 65 to 70MPH. Part of the stated rationale was that a lot of people speed anyway, but a lot of other people drive the speed limit, and this disparity is dangerous. By bumping up the limit, you're in essence telling the law-abiding drivers "it's OK to keep up with traffic" and the gap in speeds will narrow.
In my experience, the opposite happened. It seems that the people who were driving 65 before don't want to go any faster. The people who were speeding before still constrained their speed to some factor above the speed limit, and now they go even faster still. Previously, the spread was around 65-75, now it's more like 65-80.
In contrast, the interstates around DC are all limited to 55, yet people regularly do 70 there as well.
It seems clear to me that, while speed limits don't impose an iron control on vehicle speeds, they do influence it.
A sibling poster mentions studies that say it changes little if at all. Perhaps what's "clear" to me isn't true. However, I wonder just how those studies were performed. How long did they wait after the changed limit to measure the change in speed? Most traffic on most roads consists of people who make the trip regularly, and it will take time for them to change their habits, up or down.