In the UK this is extremely common. Bouncers and store security generally wear body cams. I don't think this is a huge issue, as the cameras are only usually writing to a ringbuffer. Most of the time, the camera isn't actually recording as such. In some ways, this is less invasive than store CCTV, which is usually actually recording at all times.

I think that one issue with private security guards using body cams is that there's even less guarantee that you'll get exculpatory evidence from them, as they will just delete stuff that paints them in a bad light. The police at least have procedures in place to reduce the likelihood of that happening, though how well it works in practice, I don't know.