Not that this is intentional or is even a realistically achievable goal, but limiting body armor is actually a better way of limiting the potential destruction posed by shooters than going after their guns.
Think about it; in a properly armed society, or even an unarmed society with official armed responders, the most likely force brought to bear against an attacker, regardless their weapon, will be pistols, at first. Pistols are what will end a threat in its infancy, before hostages can be taken or barricades made. But pistols are the most ineffective rounds against even simple homemade body armor, as has been seen occasionally but consistently throughout history (the LA bank robbers, and that famous outlaw character with the iron plate-armor who tore around Down Under years ago come to mind).
Anyone with any gun for the most part is capable of ending a threat up to and including a guy with a mobile belt-fed (probably the largest weapon wieldable by a single person) provided their bullets can hit vital targets. Body armor can make that flat out impossible, and it won't matter how many CCW'er or officers are around, the threat will continue while a stronger response is formed. That's why I've always thought body armor poses the greater threat to the public than firearms. If firearms have a civilizing/corrective effect by increasing the consequences for bad actors (the 'equalization' of Sam Colt), then body armor functions to remove or reduce those effects, allowing once more for a monopoly of force by the bad guys.
Now, this is not to say banning the stuff is at all helpful; it isn't, because the only easier to make in your garage than guns is probably plate-armor, and high-tensile fiber fabric is a technology with myriad uses that will permeate everything before long (I'd imagine carbon fiber makes a decent ballistic vest, for example). So, ignoring the whole 'criminals will not obey' refrain, the means to make the things will be available, regardless, so banning them is out of the picture. So what to do about this technological development that threatens to under the new balance of power wrought by civilian firearms? Embrace the arms race, and retire these idiotic, antiquated, and arbitrary rules governing pistol ammunition considered legally 'armor piercing'
Most all rifle rounds will punch through most soft armor, more and more pistol rounds are fast enough to do so, and body armor --for police, Joes, and crooks-- will only become cheaper and more available with time. When officers did not wear body armor, they got by being just as vulnerable as Everyday Joe; it's not like the presence of 'officer-penetrating' ammo sent hordes of criminals after officers' blood (and I think we can all agree that tactics was as much to blame as equipment for officer fatalities in the old days). While I highly doubt the loss of police 'bulletproofness' will lead to substantial increase officer deaths or injury (a significant increase, maybe), the important thing they need to realize is this development is inevitable. Vests will eventually be made obsolete by ballistic developments, at least for a while, so the important thing is to keep up. Part of keeping up with the criminals' capabilities is making sure non-leo citizens are not left behind in the dark ages, so that they can defend themselves as well as assist officers if needed; in such a scheme, there is less need for the officers to put their gear to the test in the first place.
TCB
), and not one demonstrator/looter/whathaveyou. Long before unrest rises to the point of shots fired, there will be a lot of tear gas, so from a RKBA balancing-the-state perspective, tear-gas rated masks are probably more important than body armor. You won't wear them daily of course, but the same can be said for all but the lightest armor.