Now compare that to regulated intersections, which come at a price of potentially longer delays of course, but in return have much lower mental tax on drivers.

Regular intersections with or without traffic lamps have a measurably higher number of incidents and rate of mortal incidents.

Roundabouts have fewer collision points and force drivers into trajectories that lead to less dramatic impacts.

https://en.wikipedia.org/wiki/Roundabout#Safety has a very illustrative diagram https://en.wikipedia.org/wiki/File:Roundabout_intersection_d... and some cited sources for that claim (claim that fits perfectly with my personal experience living near an urban intersection-turned-roundabout).