Videotaping police interrogations is routine in my state, just as private citizens recording their own activities and interactions with other people (with or without the consent of the other parties in the interaction) is routine. The practice of routinely videotaping police interrogations in my jurisdiction seems to help considerably with the administration of criminal justice.
I think the issue is that at some point those videos are destroyed, and the only thing left from the interrogation is the police officers' notes and/or memory (and that of the suspect and/or their lawyer).