I've thought about this, and wonder if the often discussed "right to bear arms" is intended to prevent the government from having such a monopoly, by which i mean is that what people are discussing and disagreeing over, wrt the 2nd amendment?
Worth considering that the original idea was the US would have practically no standing army (a navy, maybe, but not so much an army). The freedom-protecting bits didn't necessarily mean (only) from our own government, and there's a reason the word "militia" occurs—the idea was that much of our military might, were we attacked, would come from citizen militias.
Further, the right to bear arms means nothing as far as the legality of use of force. The so-called monopoly (which basically always has exceptions, anyway—it's a tool for understanding the role of government, not a law of nature) is on the legal use of force—it's not as if folks don't illegally use force all the time, so clearly there's no monopoly on the ability to use force, but on the ability to use force legally.
The really important part of the "monopoly on violence" idea is whether a state has the power to claim such a monopoly. It's a measure of state efficacy—a state fails to be fully sovereign in its territory if it cannot claim such a monopoly, that is, if it is unable to effectively quash others' similar claims; or, if its claim to the monopoly lacks credibility. Say, if a cartel claimed the authority to regulate and dispense violence in part of the US and the federal government were unable to re-assert its claim there, that would be an indication of, at the very least, significantly eroded US sovereignty over that territory, if not the complete loss of it.
A state making lethal force in self-defense legal doesn't challenge the state's claim of sovereignty, so isn't what's usually meant by this principle.
