If you are the coordinator of the worst offense in franchise history based on DVOA, you will get a share of the blame for your team's failure, regardless of how hard Robert Saleh tries to defend you.
Perhaps categorizing the 2023 Jets offense as "worst in franchise history" doesn't do justice to how awful it was. Going over 40 consecutive drives without a touchdown, and having one of the worst third-down and red-zone offenses in the history of the league certainly deserves a large chunk of the blame.
It's probably true that the Jets offense would have looked better if Aaron Rodgers' Achilles didn't snap four plays into his Jets career. A baclup quarterback better than Zach Wilson also would have helped. It is not Hackett's fault that the QB rotation behind Rodgers, the offensive line, and the receiving corps were such a disaster.
Yes, it's also true that the Jets don't get Aaron Rodgers if they don't hire Nathaniel Hackett. But that doesn't take away from the fact that Hackett has failed every time he didn't have Rodgers as his decision-maker on the field. After how poorly things worked out for him in Denver, there is no other explanation for him to land the Jets' job other than his prior relationship with Rodgers and Saleh.
The fact that Hackett is keeping his job despite the results is mind-boggling. Whether 40-year-old Rodgers coming back from an Achilles surgery will be enough to save Hackett's job next year remains to be seen.