I understand that criticism but I also have to say that in my personal experience, not having police available seems like it would hardly make a difference in my life. I have many instances where I have personally needed police because my life was in immediate danger and not once did I receive any help.

In fact, in one specific instance the police officer in question forgot to hang up the phone and on the other side of the line I could hear them make fun of my request to a coworker. I'm not too versed on political science unfortunately, but I would be lying if I said I have any attachment to the concept of policing, because it has clearly failed me and the people I know.

Edit: Of course, this isn't to say that my experience reflects everyone's. I'm just giving you some input on why people feel this way towards the police, in case it matters.

A few years ago I got mugged on my block in Oak Park (which is across the street from the Austin neighborhood of Chicago). They took my phone, $12, and then ran when I wouldn't give them my bag. I called the police, and in less then 10 minutes the muggers were in custody (I like to say they stole $12 from me and a device that tracked them from space).

We can do dueling anecdotes, but the underlying question here is well studied. Increased police patrol presence reduces crime.