I think the role of closer is overrated because it causes many managers to misuse their best reliever.
I can't tell you how many times I've seen a game where a manager uses another reliever in a very tough situation, only to save his closer ( aka best reliever) to face lesser hitters in the ninth inning, and with no one on base.
I even made posts a few times this year expressing anger with Farrell over these exact situations. There is no point in even having a closer as good as Kimbrel if he sits on the bench in the eighth inning while someone else faces the 4-5-6 hitters, just so Kimbrel can come in in the ninth and face the bottom of the order. But hey, he gets the all-important save. Assuming there was still a lead to protect.
And certainly MLB people do agree with analytics, like it or not. Bill James certainly did, since he wrote a lot of them. Former GM Jim Bowden uses them in discussions on MLB Radio Network. Gabe Kapler was shocked at how prevalent they were durong his managerial interviews (for minor league jobs, no less).They are more widespread than you realize.