You don't need to outlaw body armor to placate the american citizens. They are already being placated by the system. I don't think the system has supreme rulers as much as it's an invisible hand with incentives that are pushing our citizenry in that direction. It's just too easy to buy votes en masse, and it's too easy for corporations to buy directives from politicians, but I digress.
However, getting back to body armor, personally I don't think it should be banned. Why? Because fuck off. If the government bans it, it leads to all of these unintended consequences anyway. If I go to mexico and buy it, is that ok? If I get caught on the border, what if I say I had owned it previously? Couldn't someone make body armor from constituent parts? Are we going to ban the material? If not, could I sell the material and would it be illegal to have a PDF file (not published in America) of how to turn the material into armor? So are we going to track the material buyers?... All of this comes at a cost of taxpayer dollars, which means that I don't think the juice is worth the squeeze.
I wish that our leaders would figure out our debt, our military spending, and how to incubate small businesses. I get that there are myriad other issues to deal with too, but heaping body armor legislation on top of these primary issues is the last thing that they should get paid for.
There was once an interesting article published on child molesters, and how it is getting easier and easier to be tagged as one. I think the example cited was taking a piss in public within 500 feet of a school. So then there is a campaign competition, and if you aren't more stringent against child molesters, your opponent will be sure to mention it, even if the details of the bill are omitted... Sure this isn't even close to being the same thing, but for most Americans, I think that saying "my opponent isn't interested in who buys body armor, like Jimmy who then shot up a bunch of kids" is a surefire way to collect votes. Hence, I wouldn't be surprised if it passes...
/rant