I wish it were as simple as just putting trust and faith in those subordinates. There is also something called earning that trust and faith. Burke is practically a baby. Would you had a loaded bottle to a baby? Of course not!
Additionally, he's the Head Coach which means the entire team falls under his decision and non-decision making process.
If he just wanted to just call plays then he shouldn't have signed up to be an HC.
Also, Being an offensive play-caller absolutely gives him purview towards defensive philosophy and strategy.
Well you sorta have to give your defensive coordinator the trust and faith that they will do their job well when you are more of an offensive expert. You can't be heavy handed trying to meddle with your DC's business and then cast blame on them when things go wrong. You interviewed them and listened to their philosophy and determined if they would be a good fit. Once you hire them, you have to let them hit the ground running or fail. Otherwise you risk losing chemistry and the confidence of your subordinates.