I think the Purge is a victim of its own success.
In essence it was a B-Movie with a slightly bigger budget then one would expect. And premises like the Purge's... at first glance somewhat viable but in reality absolutely awful... tend to crop up a lot in B-Movies of that sort. Look at the wave of Western takes on Battle Royale a few years back (for a quick example, the Condemned
or the Tournament
). One can go all the way back to certain cult-film classics like Death Race 2000
to see the premise for a film pretty much fall apart with anything more than a cursory look. The difference was that those films tended to go straight to DVD or have a very limited cinema release. The Purge not only got a big release, it made a huge amount of money... but at its heart it's still a B-Movie, the premise little more than a thinly thought of excuse to set up the action. In B-Movies people tend to think past that... but because it was a success we're overthinking it.
And now to over-think it some more.
Sure, crime is legal for a night... but that doesn't mean you can't sue.
Someone steals something belonging to you? No, you can't call the police and have them get arrested/eventually prosecuted... but you could take them to civil court and get the property back + damages. Likewise if a family member were to be killed, you're going to pick up a huge civil court judgement against those who did it. Even my white collar criminal example isn't free; sure, they may "steal" all of the money and make a run for it, but their assets will soon be frozen and a civil court judgement for all the money (+ interest, + damages + costs) will soon go against them.