Notice your statement is a broad morale, and I'm presenting a consequence out here in the real world.
The math of booting wealthy people from the city doesn't play out well for the city.
It seems reasonable at first glance, but I’ve seen no proof of it. California, usually mentioned as having high taxes, still has a large percentage of the ultra-wealthy in the USA. Same with NYC. Sure some notable persons have changed their addresses, but overall, they are they hurting?
Is there any documented case of a rich-popular municipality increasing taxes on the ultra wealthy and seeing the tax levy go down?
Sort of but AFAIK nothing similar to this. There is some evidence of this occurring in Europe, notably France, but it was structural pretty different. Connecticut, NY, and Jersey often trade a small amount of residents depending on taxes year to year, but none of those individuals are really leaving the NYC economy.
NYC is also pretty unique in the availability of certain high-income jobs and amenities catering to the ultra wealthy. Like high-tax California (and America generally), the extra income and benefits from living there outweigh the costs for many. Massachusetts implemented a millionaire tax and saw a net increase in ultra wealthy individuals.
NYC is already one of the most expensive places in the country. People either live there because it’s worth the cost, or it’s the best place for them to make more millions. There is little evidence to support a minor wealth tax would change that meaningfully.