I think places where the police still walk a beat (or other regular outreach over a wide area) and get to know the locals rarely have issues with regular people. But cities don't want to spend that kind of money on these things as they would rather not tax people to pay for it. Yet it's an investment in cities' future; otherwise you wind up with this.
I think you may be underestimating how much cities dedicate their budgets to police spending:
"Mayor Eric Garcetti's 2020-2021 city budget gives police $3.14 billion out of the city's $10.5 billion. That's the single biggest line item, dwarfing, say, emergency management ($6 million) and economic development ($30 million)." (In fact, LAPD is getting pay raises while LA teachers are getting a pay decrease)
"New York City spends more on policing than it does on the Departments of Health, Homeless Services, Housing Preservation and Development, and Youth and Community Development combined."
"A whopping 39 percent of Chicago's 2017 budget went to police, and still the department got even more money, peaking in 2020 with a 7 percent increase to nearly $1.8 billion."
Note, this is, to the best of my knowledge, solely police, not even adjacent forces like e.g. fire departments or ambulances.
https://www.latimes.com/science/sciencenow/la-sci-sn-proacti...
It's great. They take the big stuff (violent crime and trafficking in hard drugs) seriously but don't have time to be running BS task forces, procuring military equipment they don't need and sitting around watching for "sketchy looking" people to harass. I'm sure it sucks to be them and they're all over worked but frankly it's great for the people.
Not being seen as jerks gives the local police better freedom of operation than the much better funded state cops who are seen as being jerks who enforce every law to the letter and nobody wants to cooperate with. I kinda feel bad for the state cops because cities like mine are where they stick the fresh academy grads who have no connections or seniority to avoid a crap assignment and then they get locals hating them for doing what the state trained them to do (also goes to show you the conflict between what the state wants and what the people of the city want).
That said, were the Real Crime(TM) to vanish I can see the local police using their newfound free time to optimize enforcement for revenue generation which would be very bad.