They had this problem for years in Amsterdam and last time I've heard about it they decided to ban moped from bike lanes in the city. Electric moped were particularly problematic because of their speed, of their silence and weigh.
I don't know what the rules are with regard to ebikes though.
At some point, we do need to restrict faster vehicles from operating in the bike lanes and the sidewalks, because the speed differentials will probably end up killing someone.