A Purge is Just Extremely Illogical
Even if you ignore the moral issues with having a Purge, all crime being legal for one night would be a terrible idea. One cannot conclude that the amount of crime committed on that night will be less than the amount committed in a year now-a-days. The only difference that we can deduce is that a lot of crime committed in one day will have worse effects than crime committed over a long period of time.
Say, for example, that groups of people end up robbing banks all over the country, which is probably very likely. I imagine that the number would be pretty significant, which could result in the crashing of the United States economy. Why would we want to risk something like that for something that probably will not decrease the number of crimes committed?