To be fair, if you asked non-LEOs how they'd feel about video (or even just audio) recorded as they do their jobs, I guarantee that more than 25% would thing the idea stinks on ice.
The opinion of people whose jobs have no bearing on the freedom of the public is of no concern in this case.
If a cop can't do their job AS AN AGENT OF THE STATE without being concerned that the public is watching, the same public who pay their wages and who the police are sworn to serve, then they need to find another line of work.
IOW, if you can't handle the scrutiny that comes with holding a job that has direct impact on the liberty of the public then you shouldn't have that job.