Trust me a day without police, right now as things are, would be an absolute nightmare. Because while the majority may act right, there will be one who does not, and it only takes one to turn everything upside-down. The sad truth is panic will ensue and then the police will need to be recalled, but with more powers that will remove more if your rights.
If something like this were to be implemented it needs to happen over a long period of time with certain mile stones in place that insure the safety of our current and future society. There also needs to be a shift in public thinking that right now would be highly improbable at best. Police, for what it is worth, are the lesser of two evils.