But also, most individuals ultimately making use of these tax havens' competitive services do not choose to restrict themselves or their businesses to said tax havens only. They tend to want to live and do business in the higher tax societies with a broad middleclass to hire from and sell to, educate their children and tend to their, say, medical needs.
I understand that one can just be(come) rich and "roll one's own" replacement for government services and eventually it's hard to see why you would even need gov't services in the first place but there will be sore losers. Otoh, I also understand that most voters would rather skimp a little on universal health insurance here, education and infra there to have a little more money at the end of the year to lease a brand-new SUV every 3 years.