Bradway is actually good at evaluating talent. He was just a bad GM. Same with Tanny. He's great when it comes to managing the cap, but he's not a football guy. Another terrible GM. You take them and demote them back to to what they're great it, and you can still help the team and not have it affect them negatively. Same can't be said for Rex.
Keeping him on as DC would undermine the new HC and would basically split the locker room in half. If the Jets decide that they don't went Rex as their HC anymore, he needs to be removed from the organization immediately.
Luckily Rex will never allow himself to be demoted. So we'll never half to worry about that.