They probably won‘t. I recently watched a talk (in german) with Julia Friedrichs, who wrote a book about millionaires and billionaires and did many interviews with them:

https://www.youtube.com/live/4HpJKPywXqY?si=bb-p558jl_otP25I

In her research she found that many of the ultra-rich people actually have deep/patriotic/nostalgic ties to their home/community and want to invest there. They often use certain tax-evasion measures because everybody else does and she argued that those few ultra-rich people who really just care about minimizing their taxes have already moved everything abroad.