I prefer the idea of a highly-qualified and experienced pilot who can put the aircraft anywhere that the highly-qualified and experienced police officer Observer asks him to. A gung-ho observer can get carried away in the heat of a chase and ask the pilot to do stuff which might be unsafe or plain silly, and the pilot needs the ability to say no.
The pilot does not need to understand a criminal, but he DOES need to know how to use the aircraft. The observer understands the bad guys. And after a short time in the job, the pilot picks up the understanding anyway.
And yes, I have been through the Copper Refinery to become a police constable after already having been a pilot for 15 years (this was back in 1982). The police training allows the pilot to carry a gun and take part in an arrest if necessary. Never had to do it, luckily.