Let's suppose that in a couple of years, data emerges that demonstrates that this happens. What do you recommend should be done about it, assuming it were to happen?

There is good reason to be concerned about this question, because a simple Google search reveals many articles on this topic: https://www.wsj.com/articles/new-york-municipalities-feel-bu...

Do you believe that taking a wait-and-see approach is wise?

Generally I don't believe that hypothetical is likely. It's one thing to see a revenue shortfall due to covid, it's another thing to suggest that wealthy people will just leave.

If you can find a case where the wealthy folks have left to avoid taxes and it made a material difference, I'm happy to engage.

Historically, the only thing I can think of is White Flight, but in that case one of the driving forces was the spending of tax money on building housing and infrastructure for the wealthy outside of cities. (And there were many other explicitly segregationist policies in place at the time to prevent the less wealthy from going along with them.)