Sworn LE officers are NOT private citizens IMO. They meet the same legal requirements as other citizens in the general public but they also took a sworn oath to uphold the law, enforce the law(s) and to make arrests when they are required to do so.
Cops are required to make arrests & to enforce the law, private citizens are not. Citizens can not witness a crime & chase someone down, then make an arrest. That is why LE jobs are called public trust positions. They have shown the ability to have morals & ethics.
Any cop who sees a crime & says; "so what" or "I'm off duty." shouldn't be a sworn LE officer, IMO.
All sworn LE officers should wear a badge & a sidearm too, IMO.
A few years ago, I saw a small group of homicide detectives from a county sheriffs office at a crime scene. None of the plainclothes detectives had badges or weapons. That wouldn't happen if I were sheriff,