The why is that they have compartmentalized their organization enough so that law enforcement can't prosecute them. There's never any provable direct links to criminal activity so members can parade around in full view without worry about arrest. If you are a member of these orgs all you do is pass money between lawyers.
Triads and Yakuza offer a package like SaaS. You pay them for all your various operational needs but they do not get involved in your business, so you are free to do whatever you want, so long as you keep paying them a monthly fee by using their laundering services, and you don't heat out the streets so much that it affects business. Everybody works with them because they have their own banks and financial networks built over decades with rules about not burning customers.
No lesser gang will run the risk of rising up against them and there really is no reason to since they are not involved in your decision making they are just cleaning your illegal profits at 30% fee and offer capital to expand your criminal operations. They also have extensive prisoner services and since every gang member ends up doing a few months for being caught with an illegal handgun you need them to pay off rivals not to kill you inside, to pay your family money while incarcerated, to offer you credit when you come out to restart a drug business ect.
Now you see where the myth of the Yakuza and Triads having millions of hitmen comes from, since all their customers are criminal street gangs it's trivial for them to organize mass violence by merely calling in all their favors through a proxy. Street gang X probably had members avoid jail with an expensive defense attorney the Yakuza provided, so being thugs they will jump at the chance to pay back the debt with violence since that's what they specialize in anyway.