>>1155839this is not quite it but almost
The greatest way to increase safety for cyclists is to increase the number of cyclists, especially regular people cycling for utility, not just gotta go fast crowd. This reduces driver numbers, adds an impetus for cycling infrastructure and most importantly increases awareness of cyclists.
Mandatory helmet laws reduce the number of cyclists, therefor making cycling in general more dangerous. They do this primarily by giving the impression that cycling is an inherently dangerous activity, scaring people away and ironically, making it one. They are most prohibitive for regular people riding for utility, as helmet use casts cycling as an exclusive sport.