I think it's kind of a multi-tiered issue. What you say is true, but police are also kind of structured in the way they are in the US because we have so many issues that we basically use them as a band-aid for, so we spread them very thin and kind of go with a quantity over quality approach. Which hasn't ended up working out very well, except in that, sometimes, and particularly for your white middle class neighbors that are going to call the cops for a noise complaint, cops appearing is basically the only thing that they needed to do. It's just for security theater, just so you can have an interlocutor that can do all the work of dealing with someone else for you, at your behest. A cop is just kind of meant to be around in order to make your dwindling population of middle class white people feel safe, more than they're supposed to actually make everyone safe. Such is why private institutions in a lot of places basically just have their own LARP cops in the form of security guards, who just stand around 95% of the time, and eat up way more in salary than they would save from product losses, or increased insurance premiums on product.

You pair this with the actual built environment in a lot of places, where cops have to be even more spread out than they otherwise would be, enforcing traffic tickets and shit like that, and it's kind of an obvious formula for a shitshow. Even if you gave police departments just straight up more money, three times as much, you'd still probably see complaints that they're underfunded, because they'd just spend all the money on hiring more people, and more equipment, rather than making a smaller number of people who are maybe better equipped to deal with, say, psychological problems that somebody might have. And obviously, in such a case, you're not going to get a better return on investment, than had you, say, dumped all the money into infrastructure that could've benefited your community, created jobs, lifted people out of poverty, and decreased the systemic causes of crime.