Yes.
No.
I'll never understand some people's rigid disdain for statistics. Goals scored is a statistic, and it's what the entire game is about. A statistic is just a way to quantify something for comparison with similar situations.
Analytics is all about probabilities - what can you do to maximize the probabilities of scoring goals and minimize the probabilities of conceding. That's where, at a base level of analysis, possession became the Wenger (and others) dream. If you have the ball, the other team can't score.
But, of course, better analysis has come along and proven that your likelihood of scoring decreases proportionally to the length of time you have possession. The "most goals are scored within X seconds of a change of possession". Because, obviously, the longer you have the ball the deeper and more organized the defence gets. At the same time, your own defence pushes higher and becomes less defensively organized and more attacking oriented - leaving you much more vulnerable when you do concede possession
What we do poorly is hold the ball all the time cycling back and around and trying to play ourselves around 2 banks of 4 and through to the 6 yard box. What City and Liverpool at their height do is attack relentlessly, but quickly. Get the ball, move forward with direct intent to score. If you don't, the ball has turned over and the opponents defense is now in transition - press and get the ball back and you're facing a much less organized and rigorous defence.
I like Ange's philosophy of not lumping it out from the back and just giving the ball back to your opponents. But sometimes an attack has fizzled, and instead of just cycling back and side-to-side, just have a fucking shot from 30 yards and turn the play over. If you haven't scored after having the ball for 180 seconds, you're probably not going to score so stop fucking about.