Exactly. And missing a 5 footer so badly that you have another 5 footer back is the same as hitting a drive out of bounds.It is all important. Driving, Irons, chipping and putting. Think of it this way. A bad shot will cost you a stroke. Missing a 5 footer is no different than slicing a drive and having to punch out. One stroke.
There's more to it than that, of course. People at my skill level are not supposed to make 5' putts every time, any more than we are going to hit the fairway every time. I don't know what the "average" range is, but I promise I'm worse than average at both for my skill level.
I need to improve both regardless of what Broadie's book or some archaic saying indicates.
The bottom line is that we all have strengths and weaknesses that are unique and we need to learn to recognize what that weakness is if we're going to put the right effort into improving our greatest weaknesses. Knowing what a common weakness is among the entire population does little to help me decide what is best for my game.
The knowledge that GIR have the highest correlation to score for most golfers does very little good if I'm already better than average with that skill (among my level) but poorer than average in others. I'm always going to suck at golf as long as I have some serious flaws in my game.
I think improvement and lower scores come from knowing your weaknesses and working on getting them closer to your strengths.