I think the most obvious point of filming police is to ensure that there is a witness if anything overly violent happens.
If the criminal kills the cop, it's recorded.
If the cop kills the criminal, it's recorded.
All police know the importance of a court, and all courts know the importance of evidence.
It's not about the "freedom to film", although that's important too. It's about the most obvious concept of filming a potentially violent confrontation, so that the truth is captured on camera, so that a court can see the truth easily.