Considering that there were reports about him sleeping through team meetings in preseason and considering he skipped a walkthrough, got healthy scratched, and pissed off his teammates because of it? (And his response - three simultaneous times - to various differing questions was "Gotta be better.")
Before anyone corrects me about the former, yeah, that much was said by the announcers of the first Bengals game (Al Michaels said, "Yeah, don't sleep through meetings, right?" after Kirk Herbstreit said, "Just a matter of being really bought into the system and being disciplined and being a pro. That’s the one question I think with him."). Burton responded, and I quote him verbatim: "I don’t even know. I don’t know where that came from. I was confused myself," but in the same interview also said: "I could’ve been better in how I’ve been handling my business in my preseason. I could lock in more on my details and the things that I did wrong, but it’s all about how you handle it. It’s all about what it means to you, and I feel like I need to do a better job of showing how much this means to me."
So, yeah, denies he slept through meetings, but admits that he tuned them and his team out. Yeah, I could imagine him getting cut very, very soon. He already had disciplinary actions at Alabama. He's already punched multiple fans (including a woman) when they went onto the field when he was a member of the Crimson Tide. He already had serious laziness issues at Alabama.
So, yeah, definitely cut, and while another team would likely take a chance on him, it's going to be with some serious caveats.