I don't really see a place for him in the NFL. One of the things that allowed Pete Carroll to work is complete autonomy over the front office and situation. Pete was a chill guy, but they also were keenly aware that he had the power to cut them at any time. He won't likely be given that kind of autonomy over a team.
The second thing with Carroll is lack of recent success in his specialty. He hasn't fielded a top 10 defense since 2016. He also hasn't won a playoff game since 2019 and his hires at coordinator had been progressively getting worse over time.
Carroll knows how to put together a program, but does he have enough time to establish culture? He would be close to his mid 70s and the oldest coach to ever coach the game in the NFL. How long do you have to bet on a guy like that staying around long term? Can a guy like that stay on top when it comes to NFL trends and changes? I'd argue the later is why he isn't here anymore.
Carroll was one of the last coaches to adopt a more modern defense. Most teams primarily play out of nickel and dime packages, Seattle played at the highest percentage of base defense as recently as 2021. This is just one example of Carroll not adapting to modern NFL trends.
The game has passed Carroll by. He hasn't proven that he can pilot a top defense nor did he hire great offensive coaches. He brings culture, but there is the question of how long does he have to set said culture, and how will the GM empower Carroll to do so?
Carroll could probably immediately win more games with a team, but long term the prognosis for a Carroll character doesn't look good. I don't think I could count on him to be around for that long as an owner.