There's freedom of speech, and then there's professional conduct.
I'd oppose a law that tried to keep them from speaking out at all, but not being allowed to bully elderly people in the nursing home where they live (and can't leave), while they're getting paid to care for said elderly people?
I don't think that's a clear-cut case of 'just free speech'.
No, but the jail time is what makes this proposal an awful idea. Saying rude stuff you're not supposed to at work should get you fired, maybe have your license stripped in some jobs but not jail time.