Yep yep. I think the most dangerous version of this failed intuition happens in places where the speed limit is 25mph. 5-10 over is the difference between a few minor injuries and a lot of major injuries or fatalities.

The exact numbers are more nuanced (both in simulation and in terms of available data on the topic), but to illustrate the effect, suppose typical reaction time allows you to slow to 0mph from 25mph just before striking a child with your car, assuming somebody with perfect training and a typical car applying proper emergency braking and decelerating at around 0.8 gs. I'll consider both the 0.5s reaction time estimate (median results in places where people are primed to have to react) or 1.5s (median for an alert driver expecting hazards occasionally). Let's assume we're going 10 over.

The fact that you were going faster means you cover more distance before you even hit the brakes. The 25mph traversed either 44.43ft in 1.92s (at 0.5s reaction time) or 81.1ft in 2.92s (at 1.5s reaction time). By the time the 35mph even applies the brakes, it only has either 18.77ft left or 4.1ft left (0.5s vs 1.5s reaction time).

Then how much can you slow down in that time? In the 0.5s reaction time case the impact speed is 27.85mph. In the 1.5s case it's 33.57mph.

In either case, you're actually striking the child above the posted speed limit in the same emergency-braking scenario, at a speed likely to cause significant injury.

Details obviously vary depending on how you set up the parameters, but 25mph is an approximate cutoff below which we empirically tend to have pretty safe traffic outcomes in residential areas and above which we tend to have pretty dangerous traffic outcomes. I don't know if people choose to speed in those situations because they don't know or because they don't care, but either way, it makes our roads much more dangerous than they need to be.