Sure. But, sometimes players get cut and do well elsewhere. Belichick is such a control freak that he might be overreacting to one bad play to make a point. The Pats probably hope to get him on their PS. Would the Hawks really be missing much by cutting Davis? Seems like he's only been good for costly penalties thus far.
I'm not commenting on Zach Miller at all. I hope he plays just like the rest. All that rest stuff is real... even in youth football. One of my sons plays in all 3 facets (O, D, ST) and is rarely off the field. His head coach chooses to keep him out of (or limit) contact in practice after some games. It's not entitlement... it's safety and wisdom.