Petty crime is rampant for the simple fact that the opportunity exists for it to occur. Most crime is opportunistic. Criminals are bold when they know they will face no consequences for their actions. An armed society is an effective deterrent. Regardless of whatever restrictions are put in place, if the society is saturated with firearms, a thief has to make a risk-reward analysis that thieves in disarmed societies don't have to make. You can go to any congested area in a big US city and there is only a very tiny risk you will be the victim of petty crime. In my experience, this is not the case in Europe. A culture of thievery exists in Europe, Asia, and Latin America that just plain doesn't exist in the USA. Why? Because 1. socioeconomic factors, 2. firearms proliferation.

There are subcultures of thieves in Germany. They are taught from childhood how to pickpocket, how to steal, how to scam--they learn to do this for a living, this is their job. They have them in Brazil. They have them in Mexico. They have them in South Africa. They have them in Thailand. They have them France and Italy. That type of subculture, for the most part, does not exist in the USA. What separates American culture from the rest is the respect for private property and the ability of private citizens to defend their property and bodies with lethal force. This right does not exist in most countries. You can go to prison in most other countries for killing somebody in self defense.