A lot of great putters let their wrists 'release' too(Tiger, Roberts, Faxon).
I don't think a flat left wrist is important. Then again, I don't think tracing a straight plane line(in putting) is as important as some would make it out to be.
For the golfers....control the aim, control the starting direction, and control the speed that the ball enters the hole.
For the teachers ... understand the influence of the club, understand the influence of the body and it's joints, and understand the influence of the brain.