First comment you've made in this thread with which I haven't disagreed.
I have coached three different sports (rugby, American football and lacrosse) and in two of them I've coached both men and women.
In my experience, SOME players absolutely thrive on kindness and gentle encouragement - the famous "arm around the shoulder" approach. Others don't buy into it at all, and work better when faced with blunt, loud criticism. The idea that ALL footballers have exactly the same psychological reaction to spectator criticism just makes no sense to me.
As a player in the three sports I mentioned, I personally enjoyed my best seasons in each sport under coaches who absolutely pulled no punches in telling me when I wasn't meeting the standard required. The year I got picked to play for Great Britain (at university level) in American football, I had a coach who chipped away at me every game, asking me why I was letting my teammates do the work for me, when I was going to actually prove I was good enough to even be considered - his best line was "you have a better chance of making the GB cheerleading squad.". Everything he said made me work harder and harder, just to prove him wrong. He understood my psychology and knew he'd get more out of me by telling me I was letting people down than he ever would by telling me he that I was a wonderful person.
Maybe getting paid thousands of pounds a week is a facet of the equation that somehow weeds out all the people who prefer the more brutal approach?