As a European, I've always thought the US had extremely high reporting requirements, power of investigation, and anonymity was dead since the NSA was invented. What makes it a tax heaven? Is it the Delware loophole only?
Having said that, it's not a tax haven if you're a US resident for tax purposes (then you're completely screwed). If you're a European with no ties to the US however (no residency, work visas, or US parents that can tie you to nationality by inheritance), then you can incorporate or stash money in the US in complete anonymity. The US won't easily (at least not on a fishing expedition) give out your information to your government. (And I'm guessing your concern would be hiding money and information from your own government rather than the NSA).
Check this out:
http://www.npr.org/2016/04/08/473477551/why-wyomings-laws-ma...
FATCA is pretty bad because it imposes a one-sided requirement that everybody report to the US, but the US doesn't want to lose its beneficial position of being the world's biggest tax-haven, so it sends data to nobody. There were calls to make the US send information to the EU and other countries, but the banking lobby has so far succeeded in stopping such initiatives as they don't want the Russian mob's funds in Miami banks to suddenly go away.