Facebook cofounder Eduardo Saverin also left the country and renounced his citizenship so that he didn't have to pay taxes from his ~7 billion dollar stock, and i'm sure there are a few other cases too.
Hmm, As far as I understand, you are trying to say, if a person wants to move to a tax haven, so that he doesn't have to give tax on his investments or assets, or business, which he had made in USA, then he have to renounce the citizenship, as if he will not, he still have to pay money. But what if he starts his business from a tax haven place. Like every document is made from that country, in this case, your county won't have to know it.
I mean I know while paying taxes you have to tell the business and earnings etc. but in this case, you still have to pay the tax, while you are living in the US but building a business from the start in a tax haven. I thought we don't have to give in this case, that's why I was confused with your statements, Well, for this the best and the worst both cases would be to name your assets to a tax haven citizen, I know it worse but still people use this method.