I expect that cost of living as a percentage of income goes down even as absolute prices go up in most cases. Whereas the taxes we're talking about here go up.
Your logic amounts to assuming you can significantly raise the price relative to other states on the basis that they already pay a bit more which I don't think follows. The degree is off but also the relative difference isn't there. Living in an expensive house in a big city is going to cost extra no matter where you do it but the taxes we're taking about will only exist in some of those cities.
Meanwhile the higher up the income ladder you go typically the fewer constraints there are tying you to a particular physical location. On the extreme end, if you make it high enough it can get to the point where you can literally relocate to a different country without much issue and it may be worthwhile for you to do so.
I don't buy it, we don't really see it on a smaller scale now despite the same incentives being in place on a smaller scale, in fact it is rare enough to warrant fearmongering news stories when it does happen and PR statements. Nobodies moving out of high tax countries to go live in Somalia without taxes. And if they do leave, then who is to say they can even maintain the same business relationship to the US? They either pay the taxes because the US taxes citizens even outside the US, or if they abandon their citizenship to avoid it then they become subject to the same costs and fines and restrictions as any other foreign persons and businesses.
I really don't really see much of any chance for downsides to 99.9% of the population, but plenty of upsides. If the only thing maintaining the US economy is a a small percentage of rich people sitting on stacks of capital, the US economy is already doomed and the people on top are just trying to be the last ones down into the water.