Some people are arguing against this by invoking the slippery slope of "What, should they also be filmed while they're going to the bathroom, or on their break? Would you like to monitored constantly on your job? I bet you've said some unflattering things about your boss during break, and officers won't get to do that if they're always filmed.".
As some have pointed out, many workplaces do constantly monitor employees. Someone else pointed out that constantly monitored cops could have problems in states where both parties in a recording need to consent to being recorded, which, even if you can argue around it, is a lot more reasonable than "how will they be able to freely spout shit that could come back and bite them in ass?".