>> results in accidents that are made much worse by excessive speed
Sure but there's no free lunch here. If you trade off speed in the non-accident cases, which is by far the majority of all miles driven, then there's a cost to that.
It happens to be a really hard to measure cost so it's always completely ignored. How would you even begin to measure the cost to the nation of traffic arriving 5 minutes later? Not all 5 minute delays are equal, e.g the cost of delay to an ambulance rushing to hospital is different to the increased cost of delivering packages.
>> the reaction time available
In fairness, you could make the reaction time measurable in hours and it'd be insufficient to prevent some inattention caused road incidents.
Another problem with only looking at speed is the unintended consequence of drivers de-rating the risks. E.g. if a vehicle was limited to 5mph, this as you know is slow enough to be fairly unlikely to cause a pedestrian death even if there is an impact, it would have the un-wanted effect that some drivers would view the risks as lower and would be inclined to engage in more risky behaviours, e.g. taking their eyes off the road to turn around and argue with a child in the back seat where in 20mph traffic they might choose instead to just speak to the child.
>> So the overall probability of accidents
No that doesn't hold. We don't have more accidents on the fastest roads in the UK.