He wants a lot of money and woody is not willing to pay it, which is why we are interviewing high school coaches like Brian Griese and Josh McClown
Kraft is known to be even more cheap, yet he wants to go there, plus Woody is not known to be cheap. I think it comes down to the good young QB. He only interviews with teams that have one: Maye, TL, Caleb. Jets have nothing there, and no prospect in this draft given #7. I do see if Ben gets rejected by NE, Chicago, and Jax, he might change his mind, but very unlikely.
Before I retired I never tried to hire anyone who didn't want to work for me. That means I never demanded they take an interview. There was never any turmoil in making those decisions beyond making sure the party knew I was interested. Pretty sure Ben Johnson knows the Jets have an opening. End of story.
The cons outweigh the pros with Rex. Yes, he's a good defensive mind, but the modern game has passed him by. Yes, he's a good motivator and players love him, but the team needs discipline and accountability right now. Also Rex specializes in 3-4 and this defense is built for 4-3. Would he really be able to have quick success here? I doubt he'd even last 1.5 years.