The reason it matters, and why the US and UK are complicit (as are Ireland and several other European nations) is that as someone hiding money you need the Rule of Law. Both countries are famous for the Rule of Law, at least in respect of the very wealthy.

Imagine a hypothetical country the Amazing Fiefdom of Jim or AFJ for short. AFJ seems like a good tax haven at first glance, they have 0% tax on offshore revenues, companies can be set up there for a modest fee of $100, you don't need to be a citizen or ever visit, they don't ask you to file much paperwork and they reject all law enforcement paperwork queries for the little paperwork they do have.

But alas, the ruler of the fiefdom, Jim, just sometimes takes stuff he wants. A billionaire who had hidden $400M and a big stake in Amazon via a company in AFJ one day discovers the company was now mysteriously owned by Jim, no way to dispute it!

If that happens with some tiny island that used to be a British colony you can get it unwound, you'll need to pay some expensive lawyers in London to make that happen so it's not an option for the average person on the high street, but if you've got this sort of "need a tax haven" money you can afford those lawyers and get Jim dragged over the coals until he agrees to give back your stuff.

This faith in the rule of law is why Russians hide money in England not in Russia. If you hide stolen money in Russia, and one day Putin wants the money, he just takes it and if anybody complains maybe they "commit suicide" by hurling themselves off a tall building entirely unassisted...