Fact is the media want simple stories. Cook isn't a good tactician, we all know this, and has had a sustained run of poor form not helped by the KP affair. Consequently the narrative is all doom and gloom.
Morgan, on the other hand, has been overshadowed by all this (which has helped him) and as there is no other real captaincy contender even with an unfit Broad the media is less likely to lay into Morgan - unless he gets the captaincy back off of Cook: then it's open season...