Even if they did want policemen of high personnal integrity, the lack of consequences for the bad ones (it's painfully obvious that a badge is a licence to kill

Even if they did want policemen of high personnal integrity, the lack of consequences for the bad ones (it's painfully obvious that a badge is a licence to kill consequence free at least once, as long as you're smart enough to do it to a minority) means people for which such a situation is attractive will flock to the profession. Tests and interviews can only weed out so many of them. Also specific to the US is the multitude of law enforcement agencies, meaning one bad cop fired from his jobs is very likely to be able to be hired in another agency, as long as he escaped condemnation, which they usually do... By making the position attractive to would be killers, and not having an efficient mechanism to get them out of the system for good once the issues are identified, it was pretty obvious what would happen...