Pro No. 2 - The team might need a young coach to grow old with
To begin the 2023 season, the Seahawks had the fifth-youngest roster in the NFL with an average age of 25.5. Seattle is likely to get even younger if they draft a quarterback in the 2024 NFL draft and players such as Bobby Wagner leave. (By the way, I don't want Wagner to leave as he has been very good this year, but all players eventually retire and Wagner is only signed through 2023 currently.)
Pete Carroll has always been good with young players, but Carroll also isn't likely to be coaching in the NFL for three to four more years anyway. He is already the oldest coach in the league and, just like players, all coaches step down eventually. The Seahawks could use a young, possibly offensive-minded, coach who grows older as the team does. That would remake Seattle's culture, but likely in a positive way.
Con No. 3 - Seattle would not have the same respect from players in the NFL
Speaking of the Seahawks' culture, it is unique. Rarely does a player leave Seattle and find more happiness elsewhere. Carroll treats his players like the grown men they are and allows them to be themselves. Players appreciate this, and Carroll is likely correct that players who don't feel treated as indentured servants play harder for their coaches and teammates, especially veteran players.
How many Seattle players leave under stressful circumstances, such as Richard Sherman, Bobby Wagner (he appears to have not been told about his release from the Seahawks in 2022 by either Schneider or Carroll), and Michael Bennett, only to return to help the team either as a player (Wagner) or a mentor in training camps (Sherman and Bennett)? One reason players don't mind coming to Pacific Northwest, which many see as the northwest tip of nowhere, is because of the culture Carroll has built. Should he leave, that completely disappears.