It's not quite that black and white. You have fixed amount of policing resources and it goes to the most impactful crimes. If crime goes down then they start caring about petty stuff. If it goes back up then they stop.
This applies more directly to something like foster care. My state is going through a budget crisis and anecdatally the result is significantly fewer kids coming into and remaining in care. It moves at the margins so a borderline case that might have resulted in removal before now doesn't.
As you note it's unlikely that some problems can be completely solved. But our resource allocation is mostly fixed or varies based on circumstances beyond whatever problem is being solved.
If this is true then a restructuring of the entire organizations might help. It seems the flaws are built in.
This is exactly what "defund the police" is (IMO) trying to say. The justice system (really it extends to the courts, the law itself, etc.) we have is corrupt. To really solve the problem that currently-existing policing purports to solve means scrapping it altogether and starting fresh, with fresh people, culture, goals, and processes.