They are definitely faster. I get passed by many old people on their e-bikes.
I would not be surprised that speed + reaction time of older people is the main cause of the extra accidents.
I cycle faster than average for Copenhagen, but it takes some effort. I'm not going to bother when I can see the lights ahead are red, or if there are too many people ahead (I may well be unable to overtake safely), or I'm going to turn soon.
Some (only some!) of the e-bikes that pass me don't take this into account. It's very easy to get to 25km/h, and I think it's easy to end up paying less attention to the street as a result. (I have done this myself, when I borrowed one for a couple of weeks.)
I think the key problem with e-bikes isn't the speed, but that you're able to reach dangerous speeds while barely paying attention to your surroundings.