I get the sentiment, but the history of Seattle actually connects better with the idea of turning the page from one era to the next, rather than shooting for “continuity” when you are trending away from being good.
Why? Mike Holmgrem retired after a successful run as HC and de facto GM after a losing 2008 season. Even though their roster was in transition, with a defense that needed to be rebuilt, they first hired Jim Mora Jr. as HC and tried to keep most everything else in place because they thought the foundation for more success with the same core was still there.
Buuuut, Mora Jr. put together an ineffective, Dennis Allen type season (5-11), which led the new owner to reset everything and bring in Carroll (in hindsight, this is type of reset is what NO needed/needs).
Carroll was able to take that very flawed team but still talented in spots team, with an older (but relatively inexpensive) aging QB and a defense that was bad, but being rebuilt on the fly, and rally them to that 7-9 record and playoff upset over NO.
If Seattle had stuck with Mora Jr. and the remnants of Holmgren’s staff and F/O, they most likely would have kept trending downward. This is why Paul Allen totally changed the coaching staff, scouting, etc.
Carroll was able to reset the coaching and culture, build the Legion of Doom,
and find his unicorn 3rd rd franchise QB in short order.
Long story short, the saga of Seattle/Pete Carroll shows that trying to maintain continuity when the original architect of it (Holmgren) is gone is a fool’s errand and once they pulled the band-aid off and actually found a new “architect “ everything started falling into place.