What exactly is the breakdown of these "rich" people by country and by dollar value?
If you know that, then you can compare tax policy amongst those countries with the most people seeking to shelter their wealth.
If you do that, AND you also compare those results with tax policy of countries with people NOT seeking to shelter wealth, THEN you might be able to come to a conclusion. That conclusion could be helpful in determining what effective tax policy MIGHT be.
You're making this harder than necessary, insofar as I can get at what you're trying to say here.
Any US dollar belonging to a US citizen that's sheltered overseas (the dollar, not the citizen) is a dollar that is removed from the reckoning of that person's US taxes.
It is in the interests of the US treasury to have the number of those dollars to be as close to zero as possible. Our tax policy should reflect that reality. If we catch people moving money to other countries so it remains off their tax returns, we assess a penalty severe enough that keeping things legal is worthwhile for the taxpayer. We give our enforcement officials all the tools and backup they need to do the job.
We aren't in the business of making our tax rate lower than anybody else's so no one tries to hide their money. (It wouldn't work at lower levels of income so why would it work at the upper levels?) That's not how the tax code is written and not how taxes have been collected historically in the US since forever. Instead, we use enforcement and penalties.