Afaik it's not so much a crime issue (the level of crime in Japan is comparable to the rest of the planet), but rather out of necessity. As (somewhat properly) portrayed in a lot of JRPGs (pokemon included in this case), due to how important the work culture is, parents in Japan tend to unfortunately be often either overloaded by work, or even actually be single parents (not necessarly separated, but if a father is called from work to move to another town, they will do it even if it means leaving his family behind).
As a direct consequences, children are more or less required to be able to be able to fend for themselves much earlier than in other western countries. That does include being able to go around alone running errands, or be able to handle housework or even cook simple things.
Due to this, they also tend to be a bit more able than normal in avoiding getting candies from strangers... though afaik expecially in bigger cities, child criminality isn't exactly rare, and it's one of the way the Yakuza does eventually get new blood.
As far as JRPGs go, from personal experience, both Persona and Yakuza series draw a very realistic description of this situation, which isn't surprising as both series are pretty big and take place in modern Japan.