A legion of people uprooting their entire life in response to a tax hike is threatened constantly in the MSM but pretty uncommon in reality.
On the other hand companies that can change their tax residency just by saying "this is our new HQ" will yes, seek out tax havens because there's almost no cost to "moving". With political will, it would be pretty trivial to enact legislation to say that the company gets taxed based upon where they actually are.
As to why that doesnt happen see my original point: A) Congress doesnt work for you B) the media acts like you could never really close these loopholes.
Overall I'm not sure if a tax that encouraged it would be such a bad thing. It's obviously against the protestant work ethic which makes it seem almost unthinkable in America but it'd probably be healthier overall.
I saw companies leaving countries for tax reasons.
I see people working 80% instead of 100% because thanks to progressive tax their net salaries remain 85+%.
Of course tax laws also factor into life decisions.