That approach is going to get people killed.
If you're not ready, able and willing to whip out a pistol and instantly put two bullets right between the eyes of each one of those criminals, you're probably better off pulling out your phone and covertly dialing 911... After you have gotten as far away from those people as possible.
> the solution is citizens becoming at least as brutal themselves
Becoming a brutal, violent person capable of ending another human being's life is a long process. It's not a switch that people just flip. Especially civilized people from developed countries where it is likely they will go their entire lives without experiencing violence.
Even if they do manage it, they'll have to pay the price. There are professional soldiers out there who are traumatized by the lives they have taken. Normal citizens will have it that much worse... And that's if they don't screw it up and end up going to prison for excessive use of force which can easily turn self-defense into cold-blooded murder.
> In any shithole society
I'm brazilian. I live in exactly that kind of shithole society. You should see the hilariously violent liveleak videos this country produces. Way too many of them are the result of people trying to fight their way out of a robbery, or intervening in a crime in progress. I remember this particularly cartoonish video where a child is running away from something, pistol in hand, and some guy randomly decides to trip him up. He gets up, shoots the guy dead and resumes his escape as though absolutely nothing had just happened.
This is a country where the population is prone to brutally lynching criminals, by the way. Ironically, the drug traffickers are the most effective at it. They routinely dispense brutal violence against the lesser criminals who hurt their drug trade by scaring off potential customers. It's gotten to the point they have formed parallel governments, complete with laws, tribunals and taxes.
I get it. The sheer audacity of criminals is offensive and the impunity is truly soul crushing. This sense of impunity permeates the life of every brazilian. It feels like there's no justice. I'm just saying that if you aim to fight this impunity, you need a far more sophisticated approach than telling random bystanders to be "fit" and "stubborn". That sort of thing will accomplish nothing but the eventual deaths of well meaning people.