Well, in most of the US, 43 out of 50 states, 5-10% of the civilian population could also be "well armed", and outside of (still) high crime areas like Chicago I think this sort of crime is much less common, and as noted by dvirsky the crime rates in general have been dropping for decades, although that's almost certainly more due to demographics than anything else (i.e. the population of young men).
My vision of a "sane society" is one where I don't necessarily bother with a sensor, although the data from one would certainly be neat, but one in which during a moment's inattention from the one with the gun, or when they stupidly ask me to empty my pockets, I draw my 1911 and give them some .45 ACP love instead of my can't lock in the first place feature phone etc. Assuming my situational awareness was so poor I hadn't started avoiding letting them get so close in the first place, a skill honed in the dozen years I lived as an unarmed pedestrian in the Boston area, yuck.
Before anyone goes off on an "oh, you're so deliciously macho" tangent, while you have to judge each incident by itself, statistically, resisting a criminal assault results in much better outcomes. If you live in Silicon Valley, well, it sucks to be you (even if this isn't your sort of thing, as it is nationwide for the 90-95% of the population who don't legally carry concealed, you don't benefit from herd immunity).
But I'm quite happy to carry one of the greatest legacies of John Moses Browning, and I marvel at how mature this technology is, where century old designs like the the Mauser 1898 rifle and the 1911 handgun are entirely competitive with the shiny new stuff, albeit maybe not quite as easy and inexpensive to manufacture or maintain.
I'd be willing to wager that simply passively handing over your wallet and phone, by a wide margin, results in better outcomes than trying to draw a weapon on a guy jacked up on adrenalin with his finger on the trigger pointed at you.
Anybody so stupid to risk a felony conviction on something so low-value as mugging someone, is probably stupid enough to pull the trigger if startled.
But I've read of accounts where citizens did things that struck us serious self-defense types as really stupid, but prevailed, and I don't judge them because I wasn't there and they were right, even if the risk struck us as too great.
Here, I'm imagining a scenario where my gun, which just happens to rest over my right back pocket where my wallet might be, wouldn't even visible to the criminals until they've got about 2-3 tenths of a second to respond, ideally where I'd also start moving laterally. And if it's night, I'd be wearing body armor (yeah, I'm paranoid :-), so even his being "stupid enough to pull the trigger" if he can manage to do so might not be the end of the world.
But it all comes down to your judgement of the situation, your luck, etc. ... and as many people have told me, you make your own luck as it were. Which circles back to what the statisticians discovered.
Honestly, one of the more astute things you mentioned was not getting into this situation in the first place, "Assuming my situational awareness was so poor I hadn't started avoiding letting them get so close in the first place," - I take full responsibility for getting mugged - it was after dark, on a deserted sidewalk - and my lack of situational awareness, directly led to the miscreants getting close enough to draw down on me and relieve me of my possessions.
I lived in a much rougher part of Oakland (17th and the lake, in 98-99) for 2 1/2 years, and never once came close to being on the receiving end of a crime, because I was always hyper aware of my environment. But, you get sloppy on the peninsula, and look what happens...
Thought personally, not living in the US, just the thought of being robbed is like science fiction to me. And it's not like I live in a great country, but things like this just almost never happen here. Gas stations and convenience stores get robbed sometimes, your apartment might be broken into, but someone on the street robbing you? I don't know a single person this had happened to.