You say it wasn't linear progression with Ter Stegen, but my view is that he has simply reached his peak performance level. He was an elite footballer at every age level in youth football and once he gained enough experience, he became an elite professional. I don't see the need for a more complicated analysis than that. Sure, Barca probably have good GK coaches, most top clubs do, and I'm sure they added to his game and improved him in certain areas, but I'm sure Gladbach and Germany have good coaches as well.
Similarly with Xavi, it's not a surprise that he took until he was 27 before he started to reach his best level because his advantage over other midfielders was his exceptional awareness of space/team mates. I would have bet money that a player with lower than average athletic ability would have to spend years playing, learning and improving his tactical understanding before being able to bring what he's exceptional at to bear at the top level.
And with Leno, it's a game of opinions, and when I watched videos galore of him in Germany, I saw a guy that was very good with his feet and said as much when we signed him because that was one of the cirticisms that was going around at that time. So I'm not shocked and didn't see a huge improvement. I also don't see how you think it's possible for a keeper to come in for pre-season in July and then radically alter his ability control and pass a football by August? In fact, from the first pre-season game he played you could see his class with the ball at his feet. Perhaps he, too, just improved with age and whilst the technical ability was always there, started making better decisions with when and when not to take a touch and in his pass selection?
And that brings me on to what a good coach can do. A good GK coach can help a little with what Leno improved on, in the same way, Arteta has worked with Sterling to improve his goalscoring. Sterling still has terrible ball striking and unreliable finishing; it's too late for much, if any, improvement to the technical aspect of goalscoring, but he can be shown what sorts of runs to make and when to make them. He can imrpove his composure in front of goal by repeated practice in training.
