The question is, however, why you want one. Are you doing it to avoid paying taxes? Are you trying to hide money that was gained from an illegal venture? Things like this are illegal, even if having the account is not.
The why is simple. It is perfectly legal to send money off shore to avoid taxes altogether. The companies are usually set up in Delaware which has very strict privacy laws and then the funds are sent off shore. They are not taxable until the funds come back into the U.S. which may never occur. When you have as much money as Mitt does and many other people there are a whole set of different tax laws. BTW the Clintons also send money off shore as well as MANY U.S. Senators and Congressmen from both sides of the aisle.
Think of it this way if you make $40 Million a year let's say you can't spend all if it every year. You keep here what you need + some for savings/investing. The rest can be sent off shore, then to another country and invested in that country. Why pay taxes on it? You wouldn't.
In answer to your other questions. Yes people use the same basic idea's for Ponzi scheme's and money laundering from the drug trade as well as other illegal activities. So do endowments and charities.
Those are the rules made by the Treasury controlled by Democrats and Republicans. No one is eager to change it. After all all the big donors to the campaigns are taking advantage of the same rules. Dont like it then go make more money. After all this is America. There is no limit on how much you can make.