Blackmail and mutually assured destruction. Morbidly, it’s not an uncommon practice for predator groups to require or have some form of collateral for a form of control and protection.
Do consider for a second, everyone on this island were committing the most horrific of crimes and were also extremely powerful people. Would you allow them to enter and leave without ensuring your own safety? No. One person spills the beans and it’s just you and that person. This is why he also recorded everything and why he had ledgers. Because it ensure if caught or reported, everyone involved would go down with him. That’s the thought process.
Did this work? No, having 2 (or maybe more) presidents, Bill Gates, Steven Hawking, and other extremely powerful people only resulted in a massive coverup. But the logic checks out in a more sane world where the elites would be held accountable and not simply allowed to control the system