Eakins is and will be the Ducks' coach. He earned his chance and the org will give him a fair one. This talk about firing him to get Babcock after 20 games is just silly pants. I swear, some folks around here spout nonsense just because they like to hear themselves talk it seems.
Babcock a dinosaur? Why, because he's been around a while? About six years ago I read an article about how he was getting his players to purposely use the middle of the ice on breakouts when such a thing was nearly unheard of. Now LOTS of teams do it, including the Ducks when we can. Some complain about his stretch passes, but that's often what you have to do when your FWs aren't doing anything constructive in the d-zone.
Analytics? I would wager that EVERY coach and GM in this league pays one helluva lot of attention to the data, WAY more than anyone here does. But some are more reserved about it than others; Bob Murray explained that of course they look at data, and they're still figuring out the parts that are truly useful. I remember when PDO was supposed to be the big indicator; now nobody talks about it, and when they do, it's always breaking it down into one of it's two component parts. Nobody talks about it because it doesn't say anything that you can't see from the components. I also remember when they said that shot location didn't matter - it was just getting shot attempts. Now they acknowledge that shot location DOES matter, they differentiate between scoring chances and "high danger" scoring chances; there are even disagreements about what constitutes a "HDSC." The analytics are evolving, and I personally respect those organizations that are being cautious about their implementation. Dubas went all-in with the high-end, high-priced skill, and they're paying the price.
Babcock is a good coach. As Pierre LeBrun noted in the Athletic, he may not even want to coach anymore. If he does, he'll find a home. But this talk of Dinosaurs and "old school" is pure garbage. LeBrun noted that he was known as a "hard-charging" coach, which may not go over well with the kids in the "new" NHL. I don't know if that's a good thing, but the world doesn't always change in a good way.