Storage/video capture are both pretty cheap nowadays. The only real issue I would worry about is too many non-police watching and commenting on too much of the footage. The public should know everything that police do in the line of duty, that said they are not qualified to quibble over the details. I am sure, with years of experience on the job, and training that has been evolving for thousands of years, there are numerous things the police are trained to do that to some amateur who knows nothing about police work would look wrong, but is in fact necessary and the best thing to do is said hypothetical situation.
I can just imagine how much "help" having everyone at the office, from the manager to the janitor, look over your shoulder and offer advice on how to do your job.