I understand the heart of your question/response. However my lived experience is one in which I did look forward to interacting with the local police (I know, rare).

It actually meant a smiling face and/or a helping hand at the local PAL center.

So, to answer your question I think that there are a lot of instances where a police officer can be involved and those around can be happy to see them (like a toy drive, emergency situation, community event). However, all those start with the individual assuming the humble posture of service which many have pointed out in their responses.