It may have been a demotion for your chap but how would it be a demotion for Wilkins? He would still have been 'manager' but the bits he obviously wasn't any good at could have been hived off to someone else. The average fan in the street (i.e. me) couldn't give a toss who was in charge of contract negotiation and the like - we just want to see the team doing well....
As for restructuring a job, if the actual responsibility and carrying out the corporate line IS a key part of the job then to restructure it without that would in effect be a demotion.
The old canard is that football managers are 'judged by results' and this obviously wasn't the case with Wilkins. I'm sure if, God forbid, we struggle under Adams no ones going to be happy if the board say "Well results are bad but off the pitch everything's fine."