Funnily enough in some cuts two handing can make the chain grab the side of the kerf (especially if have a slightly bent tooth) and make it kick. Generally it is safer, especially if you are in line of fire of kick back.
Production does matter. There’s plenty of discussion on safety vs production. Some valid issues aren’t often discussed.
In aviation there is tiers of the standard of maintenance, based on removing even the remotest chance of failure and they correlate with cost according to the purpose ie Military, public transport, private etc you go to the one that corresponds to your class and go to the one with highest quality for the one you can afford.
Tree companies doing the full complement of safety meetings and procedures with five pages paperwork on each job and mandatory rest breaks, double roping, shut down services prior to start job etc in a financially challenged environment is no longer contracting, it is volunteering... making mandatory doesn’t always make it safer, in fact I have been on commercial jobs with so many conditions and precautions taken with corresponding paperwork that I worry that I have forgotten everything actually to do with arboriculture because of the level of distraction caused by the compliance paperwork... and I believe that the full complement of safety compliance in this regard actually falls into the category of anti-competitive behaviour that serves the nationalised and large firms that have the backing and investment capability to get it regulated in a mandatory sense...
Fuel stations are the same. The big providers actually sponsor the enviro regs to mandatorily install fibreglass sealed sensor fuel tanks that cost 6 figures to create a financial barrier for new companies wanting to break into the trade...
Sometimes this paperwork and mandatory meetings etc are useful (newly assembled teams, teams with mixed levels of training etc) but often these safety culture regulations are about identifying persons to blame in the case of an accident, rather than prevent one....
There are some government lobby groups trying to address this but they face opposition from extra-regulatory lobby groups. Regulation often becomes over-regulation with non altruistic motives...
I personally don’t like hard fast rules that are supposed to be some magical armour that prevents accidents. I rather prefer to see the building of competence that can address each situation individually and react/plan accordingly, and implement satisfactorily...