The problem with carrying a firearm is that there is always a danger someone will take it off you and use it on you.
similarly if you draw a firearm and don't use it the same thing is likely to happen.
If you carry one openly you have the problem that you have to protect it, and believe me that can be a problem.
Most of the shooting incidents are robberies (Where the 'shooter, normal a sawn-off shot gun is used to frighten the robbed into obedience and to deter would-be heros) are black-on-black. Despite sensational journalism the times that the average police office would need to pull a firearm he could probably count on the fingers of 1 hand.
The balance between having to carry it round all the time, being responsible for the ammunition, cleaning it, doing firing practice on what would otherwise be your rest day, and the possibility of actually using it, would probably weigh in favour of the average sensible person saying 'no thanks'.
Remember it is not in the policeman's possession to defend himself against the ordinary stroppy drunk or for a fight in a pub. His orders would almost certainly say that he can only draw and use it to counter a threat from someone already in possession of and threatening to use a firearm. The rest of the time it's like walking around with a 2 lb bag of sugar hanging on your belt in addition to all the other shit you have to carry. Try it, it is hard work after a while and can affect your stance for years after.