Cute attempt at establishing a completely made up dichotomy but generally the politeness of a police force is correlated with how effective it is, not inversely.

The work involves more than talking with people. They do get the full effect out of being polite but their effectiveness is hurt by a long list of things. For example, we can always spend more money on it. People will always find a way to spend more money. I would scale the budget with how long it takes to do basic things. If those take much to long they either need funding or have to prioritize tasks. Things like interview the witness before GC kicks in. There are crappy security cameras everywhere but the free plan doesn't store the recordings for very long. etc There are countless stupid stories.

Talking with people is kind of most of the job though.

There's a pretty broad statement. Evidence?

Of course. In places with low crime levels, the police can afford not being completely stressed to the point they become psychos.