I can see why you ask this question. However, under most circumstances, I would not worry about this for three reasons.
Fist, people are busy. So, no matter what kind of policing is done, ordinary citizens cannot do effective policing.
Second, there are many crimes which require professionals with training, back up, and at time even fire power. In light of this the police force will always be needed in communities. It would not be wrong to say that crime has always been a feature of society.
Third, there is always the issue of detention. In other words, what do you do with people who are captured? You would need jails.
In summary, the best relationship is when the police works with the community. The only time I can see the police losing authority is when they act corruptly and unjustly.