That's an argument against always recording cameras. It's a valid one. Besides the conundrum of how a department is supposed to handle 12 hours of video footage a day from every officer they have working.
But it's not a real concern if you just have a policy that guys turn them on as soon as they start responding to a call and turn them off only after they clear the call.
Any of the quality cameras have a DVR like soft "always recording" feature where once you hit the record button it saves everything from 1-2 minutes prior. So if something just pops up in front of you it'll still be on tape in most cases. Might that catch me pissing at a gas station, yeah maybe... But it's a maybe.
The real issue with body cameras right now, for a lot of places anyway, is the laws. There are so many laws on the books to prevent someone from secretly recording you. Laws written long before body cameras were a thing and haven't been adjusted to allow them. For instance, right now I could use a body camera but 1) I have to advise you that you're being recorded (not a big deal, just a minor inconvenience) and 2) if I go in your house I have to turn it off. That may not seem like a big deal, but most calls happen inside someone's house. Domestics are especially violent and considered the most most dangerous call a cop can go on. Well none of it will be recorded!
It should just be assumed that if you're dealing with the police, it's being recorded. There is going to be a police report written so it's being recorded in some form anyway. At least then it'll be in a way that's not prone to human memory.
Someone mentioned requiring warrants to view the video. That's never going to happen. Firstly the camera is going to be property of the Department. You can make the Department get a warrant to use their own property. Secondly, I want to be able to see my own video! Besides knocking false complaints right out, the biggest draw of cameras to me is the ability to review it while typing my report. Doing a DWI for instance. As it is now I spend most of a DWI scribbling notes about how the person did on the tests. If I had body camera footage I can keep my focus on what's important and get the details later from the camera.
Guys who are against them are usually either old timers that hate anything new or guys who are worried that the public can't handle a cop dropping an F bomb during a fist fight. I disagree with both.