Only works in a society where people know each other well enough. A small frontier community might be able to ostracize someone, but not a modern city.
My co-workers don't know what I do outside work. The grocer, gas station attendant, haircutter, etc. don't know if I've done anything objectionable, and if one does the others don't. If groceries aren't paid for, the haircutter won't know. If I pay for my groceries with mugging money, the grocer doesn't know. If I'm ostracized from a given location, I need only walk a few blocks to become anonymous again. I work in a city of a million people; on the whole, they won't ostracize me...or you...or anyone else. My daily activities are spread across a 900 square mile region. Money talks; otherwise, I'm an anonymous face.
We're not in a frontier community of a few hundred people who really rely on each other. We're in a rapid-commute, mega-city, suburb-enhanced culture. If you're not welcome somewhere, just drive another minute or take a different bus...they won't know you and your cash talks.
Ostracism was once practically equal to death. Today, it means practically nothing.
You mention that a grocer won't know if I'm paying for my bill with mugging money. You are right. Of course, that's exactly how it stands today. So let's concentrate on what happens if you get caught mugging.
In the current situation, a government decides to put you in prison. The government will take about a year to do so. Result: the person you mugged is still out his money, you get lessons in how to be a better mugger, and the tax payer is charged the bill for all this. Hardly what I would call justice.
In a system of private justice, the person you mugged would sue you for damages and find a judge to rule on the case. You would have a choice: either mutually agree on a choice of judge and accept the verdict or... It would become known that you refuse to play by the rules.
At which point, you're back to looking for a place to live.
The diamond-cutting industry was once dominated by orthodox Jews who were forbidden by their religion to sue each other. So if they had a dispute, they would take it to an arbitrator to resolve. To someone who was known to be fair. There weren't any problems. It is human nature to accept recognize what is "fair" and to accept the verdict.
This is also how the English Common Law evolved. Peasants would hire judges at county fairs and festivals to resolve their disputes. The good ones got hired again by other disputants and their judgements became the basis for later decisions by other judges.