If by privacy concerns, you mean "We don't want our mistakes made public". In this case, the running over of a crash victim from Asiana flight 214 that crashed at SFO recently.
Use of force is a hot button issue, but both police and fire personnel have a lot of critical situations where not adhering to safety procedures can get someone hurt or killed. Once you get past use of force, there are more similarities than differences.
The police should be spending their time in public places, and their actions should be open to scrutiny by the public. If the police enter a private home with a warrant, privacy concerns have already been addressed by the warrant. As long as the system for cataloging and accessing the videos is open source and available for the public to scrutinize (and to check for ways it might be used beyond auditing the police themselves), where do you see a privacy problem?
Does the utility of police headcams trump privacy?
EDIT: I am playing the devil's advocate.