They do have quite a bit of pull power tbf. You only have to look at Ade, Rooney, Ronaldo, Torres, Nasri etc etc to see how they can engineer moves themselves.
But that's still not my point.
This was Arsenal specific, as the OP was being Arsenal specific. It's about the clubs goals. And what I'm saying, is that our players (in the short term at least) are the only ones that can, IMO, influence how we move on over the next few years. Because it's as clear as mud, nothing else is going to change.