I imagine most coaches are looking for 1) as much control as they can get, followed by 2) financial health of ownership. Stuff like "How many picks do you have in the 2026 draft?" or "What is your cap situation next season?" are fleeting and can be fixed, whereas the criteria I listed earlier are more permanent.
Everyone except ATL already has a GM, so they are going to be ranked lower on the first criteria. On the second criteria, ARI, LV, NYG, PIT, and TEN are all owned by nepo babies whose net worth is primarily from the team, whereas ATL, BAL, CLE, and MIA have ownership with real money on the outside.
All 32 teams are financially healthy. I agree for some coaches how much control they get is important. "If you want me to cook dinner, you should let me shop for some of the groceries"
But imagine the number one thing coaches are looking for is: 1. "Can I see a path with this team and the resources available to be successful enough that the owner is going to keep me employed" until 2) "Can I take this team to the superbowl?"
How many picks I have and what is the cap situation directly ties into both of those question. Name a single coach of the Dolphins to coach a full five season not name Shula. Odds are who ever is hired this off season will be fired before the Dolphins fix their cap situation, find their franchise QB, fix the oline and put together a defense.
As it has been pointed out many times the NFL is a QB driven league. The Dolphins don't have a high enough draft pick to draft a top QB prospect. And they don't have the money to buy one in FA. So unless you are willing to bet all your chips on Ewers being better than Maye and Allen then the Dolphins aren't a good choice.
Ross hasn't been patient or loyal to his coaches and has a tendency to fire them for the flaws of his GM.