If their budget is reduced, the police will choose where to cut services in such a way as to inflict maximum fear in the population, to cause their budget to be restored.
They will, for example, say they cannot investigate the rape of a white woman, supposedly because lack of funds. But they will have plenty of funds to harass poor and non-white people for maybe smoking pot, but mostly for being poor and/or non-white.
We can see it right now, in that they teargas, shoot with rubber bullets, beat and arrest completely peaceful protesters and people just on their own porches but do nothing about looters. It is obvious why: looting makes protestors look bad (especially if news coverage cooperates with the police's narrative), makes people scared and proves that police are necessary.
Of course, the mafia can also provide safety if you obey them and pay them. Might even be a better deal for some populations than the current police.
If you want police that work for the population and are not an occupation force extracting tribute through use of force, you need to do more than reduce their budget. You need to punish the offenders (jail, not layoffs) and replace the people in charge (their union bosses and informal leaders, not just the nominal chief of police who might have little actual power).