Would they be within their rights? Sure.
Would it be supported? I doubt it. In general, players in any sport prefer to police that stuff themselves. And that was true long before Goodell came on the scene and its not limited to football. It would need to be a far more grievous case to turn around that sentiment.
The policy and power to act against Suh and Jones already exist. That, if PFT's read is right, is what makes this odd. There is no need for new precedent. And the League has been busy for years now under Goodell demonstrating how they prefer not to be limited by uniformity and precedent.It's not hard at all to see how all your so-called counter-productive, equally miserable, and un-negotiated 'new precedents' could be uniformly applied to the punishment of obvious and repeated thuggish behavior.