Cena has about as much weight in backstage politics as any other top talent. I don't doubt that he's used his position to get what he wants a few times, every Wrestler does it, but I've never heard of him being hard to work with. That's more of a Hulk Hogan thing.
The reason Cena was shoved into everything had to do with how marketable he was to kids, as a generic Superhero who defies the odds and never gives up.
Also, even though I have a lot of nostalgia for the Doctor of Thuganomics persona, and would love the silly anachronism of a 50 year old Cena dressing like that, I agree with the sentiment that it wouldn't work. It's just too fun and lighthearted for the story they seem to be telling.