Permitting left turn on red (or right turn on red in right-side drive countries) is likely to INCREASE crashes by 10% (Elvic and Vaa 2004) with pedestrians being the most severely impacted road user with pedestrian crashes expected to increase by 43% (Preusser et al.).
Allowing traffic to manoeuvre during the red phase increases complexity and unnecessary risk. If traffic signals are required, they should be unambiguous (as they are intended).

Image credit: RAA, RAC & City of London, Ontario