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It's hard to call it an ignorant stereotype when it is the explicit policy of some police departments not to hire smart people. And to go to court to defend that policy.
https://abcnews.com/US/court-oks-barring-high-iqs-cops/story...
There is one story about one police department. Does the sheriff's department in the OP do that? Does it apply to these particular people? If you don't know, it's ignorant and it's a stereotype.
https://ny.prelawland.com/post/719662253773832192/too-smart-...
They're allowed to not hire someone if their IQ is too high. The stereotype is at the very least based on truth, and has been affirmed legally.
This really seems like one of those too-perfect Internet myths that just isn't ever going to die. I think the balance of evidence is that if you picked any police department in the US out at random, it would have the opposite of the incentive claimed in your comment, and no ceiling on general cognitive ability whatsoever.