Probably not. While a small part of gang violence deals with situations that might otherwise be handled by duels, a lot of it is more like war between factions which don’t happen to be states. Duels aren’t going to replace turf wars, even if they are legal.
https://scholars-stage.org/honor-dignity-and-victimhood-a-to...
Every boiling pot needs to relieve pressure. People need an outlet for their frustrations. Wars are far rarer, quite impersonal, and harder to shake off (as is the uniform). Even fistfight by consenting adults can get you in trouble. So many turn to crime.
Maybe there is room for a middle layer between anger and crime, between consenting adults with clear rules.
As far as I know there is almost no pre-qualification required for a private sparring session and even the qualification to be a professional is a very low bar (IIRC it is primarily a matter of eyesight, since you can't wear glasses in the ring).
It was also not uncommon for either or both combatants to simply fire their pistols into the air. Again, honor was generally deemed to be satisfied if this happened. This took some courage if you were the first one to fire into the air, as you were still required under the code to stand there and let the other guy take a shot at you if he so chose.
I'd guess the big danger for duelists would have been damage to internal organs or deep wounds becoming infected. Bullets could do this, as could the smallsword, a purely thrusting weapon which would have been the sword used in the 18th century. McBane (https://en.wikipedia.org/wiki/Donald_McBane) wrote of the difference between cutting and thrusting swords "the smallsword kills, yet you might take fifty cuts and not be disabled".
If McBane was telling the truth he certainly managed to get away with a large number of duels, though.
You can see a list of some US duels (and the participants involved) here [1]. The article also has some interesting backstory.
[1] - https://en.wikipedia.org/wiki/List_of_duels#United_States
Looked at another way, traditionally only the upper class dueled, and that didn’t change when the capitalist class displaced the feudal aristocracy as the upper class.
[1] https://historyengine.richmond.edu/episodes/view/3655
[2] https://en.wikipedia.org/wiki/Dueling_in_the_Southern_United...
[3] https://www.nas.org/academic-questions/31/4/race_crime_and_c...
The actual problems of gang violence are endemic - poverty, trauma, systemic racism, underfunded education, poor nutrition, easy access to guns, lack of role models, the romanticizing of criminality in pop culture, to name a few. Nowhere on the list will you find "lack of clearly defined rules for setting order of initiative."
We do.
But other people reject that system.
And we (in the universal sense, in this case) also have a system of resolving that dispute, and it’s, in practice however much it gets gussied up in theory, to borrow a phrase, “the strong do what they can and the weak suffer what they must”.
In fairness to your argument, I don’t think gang violence is a problem that can be reduced to zero, and think that there’s probably a low level equilibrium point that’s optimal for both parties (civil and non-civil society, for lack of better terms). So I’m probably not the audience for a total libertarian solution to the issue.
They can still commit crimes like usual.
They could even duel now, but don’t.