Plain and simple, one word...DUMB!
Any AD worth his weight in salt has a list of 4/5 candidates in his top drawer. Go open the drawer and figure out who is best. The whole search firm thing just takes too much time lets you blame someone else if it doesn't work out. I know it is the in thing to do but I am old fashioned. Arkley is right and so was JS in 2012...it's his job to hire a coach. And, he has done fine without a search firm in the past, I guess.
Hell, there have been enough good ideas for a new coach on BA. Tell him to come here if he doesn't have his own list!