This sounds crazy but this has been documented at least once, as far as I can tell. This link describes a court case where a candidate for a police force was rejected on the basis of having too high an IQ:
If you look at the culture of police in the US, the department policies that they enforce, and the laws that they enforce, it begins to make more sense. An intelligent person would not fit into existing police culture very well (because of the IQ restriction policies that have been in place). There are many police departments with awful internal policies (racist, illegal, anti-civilian), that a smart person wouldn't want to enforce, and of course so many laws in the US are just bonkers. Civil asset forfeiture, no knock raids, broken windows policing, drug evidence planting, CYA charges, these are all awful practices that are routinely done at PDs across the US, in some case documented as PD policy. An intelligent person would want to fix these problems, make a difference. This would of course hurt the PD's bottom line, their arrest stats, would cast former and current police in a bad light.
To further one of your points, there is very much pressure to keep closure rates up by pinning it on the most-plausible suspect even if you have doubts, and letting the DA sort it out. The DA does not always sort it out, and if it looks like an easy case then that someone gets railroaded.
Obviously this is not ideal at the police level (who should find the truth, not someone to blame) but some more accountability is warranted within the judicial system too. All incentives here are perverse, yet lack of them results in fuckall getting done.
https://abcnews.go.com/US/court-oks-barring-high-iqs-cops/st...