> Of all the accidents I've driven past on my daily drives, all of them happened on roundabouts.

In localities with few/no roundabouts, the vast majority of accidents still happen at intersections. Intersections of roads are the most prone to accidents (for fairly obvious reasons), with or without roundabouts.

I believe there is research showing roundabouts are actually quite a bit safer in general, but it's possible it depends on various things. But anyway, accidents happen mostly where two roads intersect, either way.