a flat amount rather than a flat rate
So a regressive tax
Under current economic conditions, economic wealth is necessary for the functioning of the economy. Some (including me) would advocate for a redistribution/government seizure of capital, but I don't know of any economist who doesn't see it as a problem if the wealth is lost altogether. If taxes are imposed on a national level, it is less likely that the wealthy will flee to other countries than it is if they are imposed on a state level. Unless the government seizes all capital, or bans capital flight, there will always be a risk of losing that wealth to emigration.
I understand that it saves money overall. I don't understand how it could save money for individual high-income tax payers. At some earning level, your taxes will be raised by more than you would pay for insurance. Even under a flat tax, that has to be the case, right? You would need a regressive tax to actually make it beneficial to every single resident.
I'm conceding that it might not always be the case. I don't have an answer to your question because I don't feel like doing the research and math to figure out what the top earners would pay in any given state under universal health insurance. It seems to me obvious that it would represent a large tax increase, and that that increase would disproportionately effect top earners. If you have reason to believe it would universally save people money, I'm all ears for a reason or argument.
I'm not sure it's even negligible between countries, but I am specifically talking about capital flight between US states, where there is a very low barrier to exit. Do you have any reason to believe that isn't a phenomenon?