There is ample research indicating that it is not correct that raising the speed limit raises the average speed by the same amount that the limit is raised. People drive at the speed that they are comfortable at. On motorways (whether Europe, USA, or here), that's normally somewhere near 120 - 130 km/h. If the speed limit is set higher than that, people won't drive faster than what they feel comfortable with.
It's true on the Autobahn: while it is true that there is the occasional high-end vehicle that is really moving along, the reality is that for every one of those, there are at least 10 each of Opel Corsa 1.2, VW Golf non-turbo diesel, Ford Mondeo towing a trailer longer than the car, and the like, and those regular run-of-the-mill cars driven by normal average people are doing 120 - 140 km/h.
It's true in the USA: Several areas out west have raised speed limits to 80 mph (a little over 130 km/h), and the carnage predicted by the safetycrats has not happened. Even Ohio has been looking at raising their 65 mph limit (still higher than us!) to 70, which would be the same as most of the states in the area. If you take I-75 to Florida, Ohio is the only one left that has not changed it to 70 mph. Carnage has not ensued. The long-term decline in motor vehicle fatality rates has continued while the speed limits have gone up.
Reasonable speed limits allow and encourage the police to take their primary focus off speed limit enforcement and onto other things ... like distracted driving, failure to stop at stop signs and traffic signals, and the like. You know ... things that are primary causes of collisions, rather than just contributing factors.
Speed limits are supposed to be set to a speed that 85% of the population will "naturally" drive at or slower than, if they are left to their own devices to set their speed (cover up all the speed limit signs and tell the cops to get lost, then measure what 100 people do under free-flowing traffic conditions in good weather. The speed that the 15th-from-fastest driver is doing, should be the speed limit.)
I would bet that our 400-series speed limits are near the 1-percentile, not the 85th-percentile.
Our secondary roads are probably almost as under-posted. Most of those posted at 80 should be 90 or 100 km/h, and there are some posted at 60 or even 50 that ought to be 90 or 100.