Actually, I've always heard that 'cop' was/is merely an acronym for 'constable on patrol', with etymological roots in Britain.
/pedantic
“I’ve always heard that ‘cop’ was/is merely an acronym for ‘constable on patrol’”
I had always been told it was from copper buttons on their coats. ‘cop’ may have been a slur at one time, but I don’t think it is now. Police have been voluntarily participating in a TV show of that name for 30 years.