This seems like an easily solvable problem, frankly. Gazillionaires don't tend to want to live in the tax havens they store their gazillions in because (surprise) they tend to be shitholes. So you just tax the movement of money in and out of the country - money is pointless if you can't spend it.

The reason this isn't done isn't because it's hard, it's because the foxes are running the chicken coop.

If that's the case, then why don't we see capital always rushing to countries that have the lowest tax rates? Last I checked Japan has lots of capital investment, a large economy, a substantial wealthy class, and yet a high tax rate...