I am not a lawyer or accountant, but I did live and work there for years. The main benefits are tax avoidance, but it's much more difficult for US citizens than for others (most countries don't tax their citizens on foreign income; capital gains laws vary).
People will make all the obligatory jokes about shady rich tax dodgers, and there are rich people and corporations that like to keep money in Cayman for ethically questionable reasons, but the majority of Cayman finance is completely legal, ethical, and above-board.
This sounds like it might be true in terms of number of individual accounts maybe, but do you think that's true in terms of overall asset value?
My guess is that there's probably much more there that's completely legal, but pushes people's buttons because they want to see it taxed at home. Like Apple's overseas billions (which are largely sheltered elsewhere, but you get the idea).
For example, in 2013 the oldest running Swiss bank, Wegelin, (itself older than the US) shut down as a result of a guilty plea for a case brought by the justice department.
https://www.reuters.com/article/us-swissbank-wegelin/swiss-b...
Sure, I understand the appeal - it's the equivalent of hiding a bag of cash somewhere and having a trusted third-party provide the location to whoever you want after your death. No laws, no lawyers, security for your wishes - exactly what you want.
"Tax issues" are synonymous with "I'm liable to pay more taxes if I'm up-front, direct and transparent with my legal structure"