Speed may or may not be the cause of accidents, but higher speed 100% makes accidents worse in terms of outcomes.
Sometimes roundabouts are found to increase accidents relative to four way stops, but they're still held to be an improvement because the accidents are on average much less severe.
While the SF bay area has been sticking silly circles into pre-existing intersections, there are many roundabouts and circles in the Northeast that keep everything moving. Sitting at a red light when there is no other traffic breeds contempt for traffic laws.
Sometimes roundabouts are found to increase accidents relative to four way stops, but they're still held to be an improvement because the accidents are on average much less severe.