I didn't ask what you would do in that situation. I asked what Birmingham PD could or could not do in that situation. You say they sure could have drawn their weapons, but you didn't say whether or not they had to. Are they required to draw their weapons in that situation?
Are you an instructor or are you certified in PPCT? While I agree that you can't strike the head with closed fists, you can and are taught to strike the brachial plexus with semi closed fists.
I admit, when I first seen the video, it looked to me like the subject was being punched in the side of the face. When we slowed the video down, you can see the left hand is hitting around the brachial plexus nearly every time. I won't argue for the right hand because you obviously don't have a great angle to see exactly where he was landing the strikes.
I was certified in PPCT. Like I said...they could have done it right, they didn't. Should they have been fired? I'm not privy to their individual service records, but I understand they were all pretty clean by word of mouth. That would factor in, IMHO, in this situation.
A few things stand out to me, and it goes to state of mind. They never once tried to cuff him on the video. The guy with the baton would probably have been ok if he'd have made his first strike then attempted to subdue him. The guy beating on his head...he was just wrong.
I suspect you're a LEO...you know like I do...the force continuum is as much about how you justify your use of force as what you actually do. They're not nearly as black and white as you seem to want to make them out (ie, if the suspect does this, you can then draw your service weapon) As a general rule they go this way:
Verbal Commands, less than lethal (which can be pepper spray, or taser usually...and different departments say which one first differently if they have both) laying on of hands (ppct), impact weapons (baton/ppct), deadly force. An officer, regardless of his department's policies, is allowed to use the force neccessary to subdue the subject, and/or to protect himself or others. Other than deadly force which requires that the user of deadly force reasonably fear for his life or another's, the officer may use one step above what the subject is using. IOW, if the subject is verbally non-compliant, less than lethal is ok. If he's physically combative but unarmed, the officer may lay hands on him, use less than lethal, or impact weapons. In the end it's all about what he can justify by what he says he perceived.
FWIW, drawing your weapon is nothing more than verbal commands in the force continuum...until you use it...an officer can draw his weapon any time he thinks he might need it. It's when he uses it he has to justfy it.