Simple solution: Financial Transactions Tax. A .001% fee on all stock, commodity, and FX market transactions would bring in over a $Trillion per year. Quoting: Anonymous Coward 2164937
Effect on markets would be negligible, and would reduce computer HFT (high frequency trading) that presently controls and distorts the markets. Since everything is automated, the tax could be automatically deducted and electronically remitted directly to the IRS. Problem solved.
The amount matters, and if I recall correctly, about 20 years ago James Tobin was recommending a tax level of .01%, so your suggestion is at least milder than that.
Still, the effect on markets would not be negligible. For example as you rightly identify, it would drive away high frequency trading. It wouldn't shut it down altogether, some would survive and move to different jurisdictions. It would weaken NYC (and Chicago, Philadelphia, etc.) in its ongoing battle with London and potentially other places (Shanghai?) as the world's main financial city.
And to the extent it reduces taxable trading, the tax receipts would be reduced too. Don't calculate that on current trading volumes, since you say, even boast, that those volumes would go way down.
The rich people who are successful in financial markets consume a lot of goods and services, many of them domestically. If they move out of country, you may say good riddance but do you mean it?