This is a very wrong way to think.
He had zero experience when he got the Barca job but that was 2003. It took them another 3 years before they started winning consistently again, then there was another bump in the road until he insisted on hiring Pep Guardiola.
Now, the same guy he's at Man City(our City rivals) competing for every trophy with us. Hiring a rookie to stop them is not a wise decision - his rookie position in 2003 does not apply in 2021. To even have any chance of competing with them, hiring a DOF with a similar wealth of experience is a great start.
Worst case scenario, If Murtough fails, Wooward could also as well cancel the role completely and argue life was better without a DOF than with a DOF. He would say he was reluctant to even create the role in the first place and only gave in when the fans won't stop moaning about it. It's Ed Woodward we are talking about here, he's a slithery creature.