How would this stop "all crime"?

just wish that they had said something like "all VIOLENT crimes" have stopped because of the purge"

Of course the crime is just at 2%, the movie explains it clearly: Step 1: Instate the Purge; Step 2: Step 3: End of all crime!
It's the stupidest premise for a dystopian story ever. But they show the rich people as sick, perverted sadists, so dumb people can pretend it's a deep commentary, some *beep* social allegory or whatever. Ethan Hawke seems to love these movies. I have an image of him preaching young characters in that "wake up sheeple!" pose in the middle of the room, pointing to the window, saying that out there right now there's people dying because some serious social issue and yadda yadda yadda.
I was hoping for a break in the mold of "rich bored people getting psychotic", when the family is "saved" from the invaders near the end, but no! Rich people live lifes of appearances, sheepel! They will kill you because they're jealous of your garden ornaments! They are all sociopaths without souls!
Then I was hoping that we would se some of the psychos being murdered in some very painful way, scared, regretting having been evil bastards, getting an axe on their butt cracks, but noooo... Hollywood movies always have the psychopaths either be dismissed with an unsatisfying bullet in the head, or the main hero shows himself above mundane things like justified painful retribution. These movies just serve to make you angry, without that cathartic release of seeing the bad guys really get what's coming to them. Even movies that try to do it end amping up their actions to a grotesque level, making the good guys'revenge lame in comparison.
My kind of ending would be the mother sending the kids to their rooms, waiting for the Purge to end, and THEN saying something like, "Take these smug relief smiles out of your faces. That siren is not your ticket back to the civilized pretty world, mf'ers. I don't need this *beep* scheduled time to end you all, nobody knows you came here, the authorities will be busy for the next days trying to identify everyone that died. Time enough to make you suffer. That's what MY idea of contributing to a better society is."
Now, THAT would be an ending worthy of the name "purge". They didn't even have to show gore, just make an end credits montage of common kitchen appliances with the minimal blood dripping from them. To keep things classy, you know.

What about all the pedophilia and child rape that happens during those 12 hours? I know a lot of sick people get their kicks doing that...

Agree, it's by far the biggest flaw of the movie and the stupidest assumption of all. Not even mentioning the fact that how the hell did violence go down 2% if on that one night there was probably more violent crime than there would have been on the entire year. Clearly they're not counting that one night on their statistics so everything about this idea could be completely destroyed with some logic.

It does not stop crime because people get a release. It lowers crime because they're simply eliminating lower income people and the social problems that occur in their neighbourhoods resulting in crime. The second film explains that it's simply an excuse to kill the poor and the government officials are actively involved in their execution.