Why was the Japanese government far more tolerant of the Yakuza than the American government of the Mafia?

It has been in my understanding and light research that Yakuza simply holds more power then the Mafia ever did.

Let's begin simply. The Yakuza formed in the 17th century. This is compared to the Mafia forming in the 20th century. Now one must identify the times of both the formations. Japan in the 17th century is far more turbulent then America was during the 20th century. Simply analysing from that time period, we can reasonably observe that the Yakuza formed at a time when they could efficiently and effectively grow. Once this is established, we must look at the way the Yakuza grew. It formed very gradually, starting with petty crime with few leaders, until slowly growing to involve the idea of division of labour, resulting in more leaders. As the organisation grew, it elevated it's crime as necessary, not out of want. It should also be noted that the Yakuza was not only located in one part of Japan. It spread effectively across the country.

The thing that makes the Yakuza so effective is the culture they cultivated. They built up a society that was willing to adapt to it's circumstances, most evident following the 2nd World War. The Mafia was a relatively small crime syndicate, and did not spread effectively. They engaged in gang wars, which effectively destroys themselves so the government doesn't have to. They formed a community that simply isn't sustainable. Killing became a foundation of their society. The Yakuza realised that if this became to big a part of the society, it would destroy themselves. The Mafia did not an in turn led to their destruction because they did not understand the principle of sustainability. A community cannot last when killing and war are too powerful a part of their society. They will eventually be eliminated by the principals they used to guide themselves.

For further reading, I recommend reading "The Yakuza, The Japanese Mafia" By Anthony Bruno. It is available to read here: http://www.crimelibrary.com/gangsters_outlaws/gang/yakuza/1.html Sorry no hyperlink, on mobile.