Trials are already public. Typically transcribed and recorded, even in states that still ban news cameras.
Teachers aren’t typically armed and don’t have the power to kill someone essentially at will.
As far as hospitals, most surgery requires the patient’s informed consent, and information on surgeons and doctors is actually available to the public. A bunch of cops jumping on someone, not so much.
Police need special oversight. If they don’t like it, they’re free to find another job. Frankly, the country would be a better place if 50% of them quit, and enforcement was restricted to serious crime due to lack of manpower. Over the top? Maybe. But we’ll have to agree to disagree.