Our society has taken the concept of law enforcement and turned it into nothing more than a mechanism for providing taxpayer-funded security services. That's not was law enforcement was ever supposed to be in the U.S.
If you go back and examine the historic role of a "law enforcement officer" in this country, you'll find that such a person had no pro-active role at all like the police have today. The typical county sheriff wasn't appointed to walk around a jurisdiction and make arrests or hand out citations whenever someone broke a law. The term law enforcement did not mean "ensuring that the citizens obeyed the law" at all. Instead, law enforcement meant "enforcing the orderly application of a legitimate legal process." The role of law enforcement wasn't to serve as a publicly-funded pain in the @ss, or even to protect citizens from each other . . . it was to protect the accused criminal and ensure that he/she was subject to a lawful legal process.
In other words, arresting someone wasn't a mechanism for protecting the citizenry from a criminal . . . it was to protect the criminal from an armed citizenry that was likely to have a predisposition for hunting the accused criminal down and enacting their own version of "frontier justice" on him.
I see this argument made from time to time. Perhaps it’s my lack of understanding as you say, but if you think your concept is a good idea, I would urge you to look at places like Somalia and how gangs have been elevated and warlords rule the day.
It would take about ten minutes before our cities would devolve into total anarchy.