1: Not convinced that "eliminate crime entirely" is a feasible goal outside of fundamentally changing what humans are. Which we probably won't be able to accomplish for the next, what? 10-15 years? ;P
Greatly reduce crime, and the kind of crime which would call for an arrest, sure. That mean greatly reducing the need to make arrests, not eliminating the need entirely.
Most people are not monsters, most people are not inherently evil, they gotta learn that shit. I lived with a monster from before I can remember, I couldn't stop him from hurting my mom, so I made sure he saw me seeing him, and when I learned what police were in theory I tried asking a neighbor to call them to help one night when he got especially violent (we had no phone) and said neighbor responded to the 4 year old from next door asking them to call the cops in a reasonable enough fashion by calling the cops, who came and removed Jackie from the house... until that morning when he came back home.
Next time they came and asked them to keep it down basically, I tried to plead with them to help because I couldn't stop him, tried to explain this, and was told that I should go back inside, it was late.
Just because something is wrong doesn't make it a crime apparently, but I knew that if I killed him, even though it was the right thing to do, it would probably be considered a crime so I started working to figure out how I would have to do it to avoid getting attacked by the people who should have helped in the first place, and thankfully before I was big enough and capable enough to do this he offed himself while my mom was living where he couldn't find her.
I know evil, I know what monsters actually are, I can barely stand to watch Alien because it is such a goddamn visceral glimpse into my childhood: being trapped somewhere with a monster you can't stop as it threatens and attacks those you care about.
I honestly and genuinely hope nobody ever has to stare into the eyes of something like him, and it is a rare thing indeed to come across pure psychopaths in the wild.
Sociopathy is what happens when you tamp down anything inside you that says "stop this" and begin trying to emulate monsters, but it is generally a learned process that can be unlearned. A sociopath might end up being reformed and learn how to function normally again, a psychopath just learns how to hide better so they can keep playing with their food. People need to be protected by people who know how to identify psychopaths and either train them via game-reward strategies to behave (negative incentives will not stop a psychopath, let them play a game of slots on a computer and tweak the slots so each win causes the next one to take twice as much time or more before it happens, most people quit playing rapidly, a psychopath doesn't think about the negative results and keeps chasing the positive ones, give them points to hide themselves, bonus points for not doing things like hurting people physically or mentally, it is a promising method apparently), or remove them from society if they can't be manipulated like that.
Without laws that criminalize things only if they're done by the poor or darker skinned portions of a community, without opportunities being deliberately limited for them, without mental and physical healthcare being made prohibitively expensive, without housing and food insecurity, the vast majority of crimes would literally disappear overnight.
These aren't people doing things because "man, I bet it'd be fun to break into that building and steal a TV so we can get a gun and some drugs to go shoot some people while stoned" or something like that. You try to steal a tv so you can fence it and you try to use some of that money to get high because it makes it a little easier to ignore the nagging soreness in your jaw, the clicking twinge in your knee, and the vague feeling everybody is watching you because they know what you were thinking about doing.
Even in the case of cops, most of them need to be indoctrinated into the mindset of "every call could be your last, nobody but your partner has your back out there" before they start bragging to other cops about fucked up shit they've done or viewing it like a game of trying to get people to fuck up so they can arrest them. Then after you get someone in that mindset you task them with responding to a huge range of situations with a limited set of skills, if all you have is a hammer, everything starts looking like a nail... if all you have is pepper spray and a pistol...