They tried back in 1964 which only lasted till 1965 when the Yamaguchi-gumi left. Since then there are factions of the Yakuza having social gatherings, meaning some groups are affiliated with other organizations on a board. These are the Kanto-Shinboku-kai, Yonsha-kai, Gosha-kai, and the Kanto-Shinno-Doushi-kai all still active as the others have disbanded over the decades. Think of them like how the American LCN, Sicilians, Ndrangheta, and Camorra are structured. Tokyo is still the hot bed for the Yakuza, which is why the Kanto-Shinboku-kai and Kanto-Shinno-Doushi-kai have the biggest influence there.