I agree - USA is great for account opening for non-Americans but it does require personal visit.
Quickly, here is why the USA is a great jurisdiction for non-Americans:
They have FATCA but that is other countries reporting on Americans. They don't have anything in reverse (they are not part of CRS and with congress and senate and white house being controlled by Republicans, this won't change any time soon). So in a way, the USA is kind of being hypocritical by expecting other countries to report American foreign accounts, but will not report the citizens of other countries...
However, there are two instances where, while you may not be reported, the banks will supply paperwork to the IRS: 1. if you have a personal interest bearing account that nets interest of $10.00 or more every year. 2. My mind draws a blank on the other criteria right now since it is middle of the night here...when I remember, I will update this post.
That being said, just because the banks provide IRS with that info, doesn't mean it will be exchanged. Right now there is no mechanism to force information exchange...
USA also has many stable, long standing banks with access to one of the world's strongest markets.