There is a possibility that Mayo met with the Suns brass and they were completely unimpressed with his character. With Beasley on board they may not have wanted to bring in another potential headache that could lead to a toxic environment. You get enough of those kind of guys and it's bound to lead to suboptimal chemistry. Telfair had a poor reputation as a teammate if I remember correctly, but seemed to be great when surrounded by great veterans like Steve and Grant last year. We no longer have those veterans. I, for one, kinda like Mayo and think people are overcritical of him, but my perspective is obviously ignorant as I'm not privy to much information with former teammates etc.
Mayo got beat up by Tony Allen in a fight that all indications are he instigated. He supposably broke a teammates jaw in college, and his team (seemingly) couldn't wait to move on from him. Taking one of these guys on is risky, but taking two on can just be ignorant or unintelligent.