As far as I can tell that's not at all the case in Sweden where I live, in fact geriatric or slow drivers are very rarely involved in accidents. Intoxicated drivers are extremely rare compared to most other countries. See e.g. https://www.itf-oecd.org/sites/default/files/sweden-road-safety.pdf which says "Inappropriate speed is one of the leading causes of road crashes". You can find more research saying similar things on Google, e.g. that for every 10 km/h increase, the risk of an accident increases by 33 percent.

But it's not just a matter of having a high overall speed. It's also how quickly you accelerate / break. BMW/Audio/Tesla drivers have a high capacity for acceleration and they use it e.g. to overtake in situations when others wouldn't. I suspect the cause/effect is the other way around though: if you're a reckless driver who doesn't care about safety, you're more likely to choose a car that has a lot of power.