Realy good thread this, very interesting reading. I would offer a coaches perspective on it.
I believe football should be played in a certain way, and that is possession based with patience and a bravery across the pitch. I like my defenders to be comfortable receiving and playing short sharp passes, for example. I want strikers who drop in and play. In my opinion players play football to be on the ball, and I want them to experience that. I want technically gifted footballers everywhere on the pitch, ideally who can play on the half turn and with their head up. That, you might say, is my philosophy. I am an all in fan on how Brazil 82 played.
With that in mind I will think about the data I think is relevant to that style of play. So possession stats, pass completion etc. I dont really care about others like running stats, or XG, or tackles made etc. Now data access is limited at the level I coach, but I make use of it. I sit down after each game and write up my own sense of how the important data aspects felt in the game. That then gives me a basis for my next couple of training sessions. What I wont do, and perhaps this is a weakness, is change the way I want to play. I will always be consistent in that and the data helps me focus on how to improve the players in that style of play.
I suspect people like Ainsworth, as he has been mentioned, are similar in some ways. He has a style of play that suits his means and I suspect he focuses on stats that suit him. Maybe things like territory and final 3rd touches, set pieces, duels won. I actually think he is one of the best tacticians in league 1 and his results are remarkable.
My guess is coaches all have a preferred style. They will use data and stats to help them identify how best to improve the team, or who to sign. The higher up the pyramid they will be used to understand the opposition, as the op points out excellently.
Good reply... pick the stats that suit what you want to do...