Cena always does what Vince tells him to do. I've never heard any dirt sheet news that Cena tries to influence the booking - He just does everything the company asks him to do and eats, drinks, sleeps, shits, and breathes WWE.
When he was filming some of his movies, here is more or less how his Monday was (2 hour RAWs back then)
3:00 AM - Wake up.
5:00 AM - Filming starts
12:00 PM - Filming stops,
12:00 PM - 5:00 PM - Make a Wish work (includes air travel)
5:00 PM - 8:00 PM - Plane to WWE event location and preparation
8:00 PM - 10:30 PM - RAW + overrun
Then he'd get back on a plane and travel to the filming location, getting a few hours of sleep on the plane and in his hotel.
If he is booked to no-sell a 4 on 1 beatdown and a DDT on concrete against a dominant stable, that's what he'll do. No questions asked. If he's told to fly to 3 or 4 different cities to wrestle, film movies, and do Make A Wish work, he'll do it. If his marriage and friendships outside of wrestling are weighed against being a WWE corporate slave, he'll choose WWE, always.
The problem with Cena is that he has the power to influence the product for the better but he doesn't do it. He doesn't try to get other people over in the back, nor on the mic, nor in the ring. He's a complete yes-man.
Since he's viewed as the face of the company, Vince wants to shoehorn him into every hot feud... and Cena goes along with it. He doesn't do things to screw over the rest of the roster on purpose, but he lets himself be pushed to the detriment of everyone else... and he's respected so much by the rest of the locker room that no one blames him for not going out of his way for them, I don't think.