> The customer service experience of criminals isn't the right thing to optimize and probably has nothing to do with outcomes if not inversely correlated with crime reduction.
The vast majority of contemporary approaches to policing, but dating back to e.g. Peel in the mid 19th century, run quite contrary to your ideas. The people that police interact with and "the broader community" should not be any different (this basic idea is called community policing), otherwise policing will inevitably fail to meet community needs, for several different reasons. It is fairly well established that a lack of contact between police and members of the community results in an increase in crime, for a few reasons but in particular because the community will stop reporting crimes to the police if they do not have positive interactions with them. This has been a widespread problem in most if not all US cities.
In practice, the portion of people that police interact with who receive any sort of legal action (from citation to arrest) is very small. Around 2% in one field services division. The vast majority of police interactions are either addressed by policework (collecting information, brokering agreements, just telling people to knock it off) or were not even potentially criminal in nature to begin with (traffic accidents, medical emergencies, etc). These are all cases of officers acting as individuals to address a problem, with no criminal process involved.
> If you're ever talking to a police officer you're obligated to follow their lawful commands, and if you have any issue with them the forum to litigate that is court not with the police or through something like a net promoter score.
It sounds more like you're talking about a prosecutor. Police officers exercise a great deal of discretion and individual responsibility outside of the legal system, and are accountable to the police department for their work. Police departments have an entire command or division, usually more than one in practice, responsible for reviewing officer actions and conduct. Police departments are organized under city and state governments (and occasionally some other less common kinds of governments like improvement districts), and are accountable as a whole to the government they derive their authority from. That is, while courts do serve as an ultimate forum for complaints about police, courts generally only address specific violations of the law. Broader policing issues are heard out in the chambers of city councils and legislatures.
> If anything the experience of the people not interacting with the police aka the broader community IS the thing to optimize for. Maybe mail out surveys and ask people where the police are doing well and where they could be more helpful.
This is a standard practice in large police departments and is usually more formalized through e.g. commissions and councils of community members. Surveys themselves often originate from the city government in its role overseeing the police, e.g. conducted by the mayor or council members.