Considering you have already implemented many private versions of polices- voucher system/tax credits for healthcare and schools, private prisons, etc. - which allowed the player to eliminate policies in Democracy 3 (state healthcare, state schools) that were locked in place in previous versions, would you consider doing this for police as well? It is not just a left wing concept; libertarians have talked about private police for decades, bringing up the issue of police having a monopoly on enforcing the law, of which the lack of competition may have something to do with why they are not held accountable. I am not necessarily in agreement with abolishing the police or inviting competition in enforcing the law, but there is validity to the argument in both left and right wing circles.
On the more extreme ends, left wing points out the very high cost for government to maintain the police force and suggests alternative ways to spend the money as OP mentioned, usually wanting a softer touch, less punishment; right wing agrees with the high cost argument but doesn’t agree with having a softer touch necessarily, just is against big government inefficiency, waste of taxpayer money and enforcement of laws against liberty (like civil asset forfeiture).
Potential policies could include greater armed security/armed security services market, citizens arrest, bounty hunters, (which are linked, giving armed security some legal teeth to arrest) as a way to abolish the police (cancel the policy) but still enforce order. Also, potential policies like the OP mentioned that reduce the need for arrest and reduce what is considered to be in the criminal realm could reduce the need for police.
Another idea more within the mainstream is that regions still pay for police, but they can swap their security service, so that police forces that are racist/untrained/not responsive can be swapped for better companies; very similar to how a region/city can change its trash service or parking services, choosing to contract it out. Since in Democracy we have more of a birds-eye, federal view, we could choose to leave that up to the regions. And this is more realistic anyway, since in the U.S., while the federal government is involved with police, it is mostly left up to the states and city governments to decide how to enforce the law and how much to spend.
Abolishing police would make gun rights more of a flashpoint issue in countries where guns are more restricted, as even in those countries there is strong belief in a right to self defense, but a major reason given for gun rights restriction is that police alone are sufficient for defense, and that only police should have arms. In the case of police being abolished entirely with no alternative services, only citizens themselves can enforce their protection against violent crime and the government would only be involved in court judgment, so I believe calls for gun rights would increase.
Although it would be vastly different than the world we live in, I could imagine a world in which people can decide if they want to pay for security services, especially in the United States where gun rights are Constitutionally protected and some do not even expect the police to arrive in a reasonable amount of time in an emergency.
I could see this being more of an option as the Overton Window is moved very far in the Liberal/Capitalist or the Liberal/Socialist direction. In libertarian playthroughs, I often like to have lax drug laws, prostitution, low taxes etc. but still the police force is high when there could be alternatives.
I agree with you Cliffski that in mainstream thought, it is not even an option, but the Overton Window idea that you’ve added has given way to interesting first-time additions to the game.