Funny, but I always thought Pirri's best chance of sticking with the team was if the Hawks had signed somebody like Boyd Gordon. Currently Q doesn't use the third line (when Shaw is centering it) as a checking line. So either the second or fourth lines have to step up and play against a tougher line than they have in the past.
As an example, when Kruger (early in his career) centered the Hawks second line he was taking the shifts that Shaw is taking now. If an actual checking center was on the third line then Pirri could be doing what Kruger was doing then. So now he either has to either beat out Shaw for that role or play a better two way game. And sometimes players like Shaw who are more multidimensional can take an offensive slot away from a better offensive but more one dimensional player like Pirri.