For example, this piece from The Week notes that the idea for the Purge came about after "a public outcry for protection and vengeance against the increasing number of homeless." That's important (relatively speaking), because most of the talk about how ridiculous the idea of a Purge is centers around it being sold as a way to decrease crime by allowing average Americans to let out all of their pent-up rage and anger once a year with zero fear of punishment. While it obviously evolved into that at some point, what this forgotten detail reveals is that the program started with a very specific target and goal. It wasn't to reduce crime by giving people the green light to act like savages; it was a declaration of war against the homeless.
The Purge: Election Year
It's like Halloween with firearms!
Sorry to have to be the one to say it, but that's an absurdly easy war to win. That's especially true if a combination of high-profile crimes committed by homeless people were coupled in the wrong way with a propaganda campaign which painted the poorest members of society as the greatest threat to the well-being of average Americans. It's not like there haven't been several examples of tyrannical regimes that achieved their goals in large part by convincing the people they ruled over that one particular segment of society was responsible for the ills of everyone else, and thus should be removed entirely. What you see in The Purge, at least at first, started as just another example of something that's happened plenty of times before. It's just that in this case, the targets of the "cleansing" were the homeless instead of a particular ethnic or religious group.
What would make the Purge especially successful is that the enemy in question would have almost no means of defense. It's not like homeless people have the guns in this country. If the United States government convinced the public that homelessness represented a grave threat and gave them 12 hours to go out and deal with that threat in any manner they saw fit, the result would be nothing short of a bloodbath.
The Purge: Election Year
And a boon for the novelty assault weapon industry.
In that way, at least for one year, the Purge would be hugely successful. Homelessness would indeed be much less of a concern, because untold numbers of homeless people would be wiped out in one night. How to justify its existence after that first year is an entirely different story, but the government would have public opinion on its side for at least a little while after the inaugural Purge. That's because ...