So far as I can tell --- and someone challenged me on this recently, saying they'd been in court over a case related to it, so take this with a small grain of salt --- this "too high IQ" thing happened once, in New London CT, and if that's really the only documented case you have to wonder whether it wasn't just New London making an excuse for why they didn't hire someone they just didn't like the vibes of. I can say with assurance that there's no "IQ cap" in cop hiring around here; there's a standardized assessment, and there's no score cap on it.

I wince at the disrespect shown to the profession on message board threads (in part because it feels like a self-fulfilling prophecy, and in part because it's so clear that the people expressing that disrespect would be less happy if they couldn't make these arguments --- i.e., they want policing to be bad), but normal people love police. Our resident beat officer showed up at our block parties and was a minor celebrity.