Your reply assumes that [High IQ] => [Good Police Officer], but the argument in the US is that [High IQ] => [Bad Police Officer[1]].

I don't agree with this personally, but what they are doing is not equivalent to them exclaiming that "We don't hire the best". It would only be equivalent if they were explicitly filtering-out qualities they believe contribute to being the best, such as discipline, strength, and the like.

[1] Due to boredom, etc.

Having worked for a public utility, there is a fair share of mediocre people but worse yet there are people in management positions who are entirely incompetent and can't recognize/don't know what to do with good talent. Funny enough, some of those people ended up working for Amazon.

I once heard it said: government jobs are welfare for the middle class. IMO it's not 100% accurate but it's better than 50%.