Teams have been using analytics, and successfully, long before the Mets started using it. Perhaps "old school fans" want the Wilpons back? Then again, the Wilpons had their best success when Sandy Alderson -- who had been part of the front office that started analytics -- was running baseball operations.
All these data still need to be interpreted properly, though, and I think a lot of teams are blowing it in that regard. On a very basic level, Peralta had consistently been a 3.50 or 3.60 ERA pitcher with the Brewers, until he had a very lucky BABIP last year. People with a 100-level understanding of analytics would know better than to make an offer for him like he were an ace. In general, teams have adopted the Rays' approach to handling pitching (maximizing speed and spin rate), which was basically designed to eke value out of AAAA pitchers before their arms blow out, and applied them to good pitchers who are now pitching five innings a game and still can't stay healthy. And if there's clear evidence that pitching is better as a whole for it, nobody has presented it.
On the bright side, the Mets' rookies are doing fine. McLean had a stretch of adversity, but that was inevitable and he overcame it. Scott is doing well, and Thornton has been an unexpected surprise. Plus Manaea seems to be putting it back together. Holmes' injury may have killed the Mets' season even more than Soto's trips to the IL, but it was a freakish in-game injury that had nothing to do with his right arm. I'm not about to take it out on Willard for Peralta not meeting expectations that he wasn't a good bet to meet anyway.
And honestly, if other GMs want to overpay for Peralta, I'm cool with that.