Speaking strictly for Americans, this simply isn't true. There are very, very, very few benefits to keeping your money offshore. Tax fraud is benefit #1. "Asset protection" (which generally means you're hiding money from your spouse or business partners) is benefit #2. Unless you actually own property in the country where you keep your money, or do real business there, those are basically the only benefits. There are also massive costs: (1) the literal costs that the foreign nation (and bank) will charge you to hold your money; (2) the risk that the money will actually be available when you want to access it; (3) the risk that the foreign government and bank will cooperate with the U.S. government when it comes knocking (this risk has greatly increased since the passage of MLAT and other recent treaties).

I could definitely see how citizens of other countries could legitimately use such accounts to get around immoral laws in their home countries. Whether this makes up "most people" who use offshore accounts, as you claim, is beyond my knowledge.

I would bet that a great percentage of the volume of money moving through these offshore havens are indeed a hedge against insolvent governments: the governors' own. There's a reason these island nations are where despots like Gaddafi, Mugabe, Marcos, Bashir, Afwerki, Mbasogo, Mubarak, Kagame, and others, and their extended families, park their money.