It's all about money. The amount of money you bring, where the money comes from, where the money is going, and how much money the bank can make. That is then set in relation to the risk profile of the applicant.
There are Cayman companies/entities banking in London and New York. It doesn't mean some random person has any realistic chance of showing up with their Cayman company. Those companies that have accounts there have them because they are part of VC or PE structures, investment vehicles for very wealthy clients, and so on and so forth.