reducing the tax rates to match the havens?
Because that just won't work. There have to be countries with infrastructures.
Tax havens are typically little places that can't actually support those who live there on paper. Maybe they can support the individual robber baron, but they can't support the workforce that makes the robber baron's wealth possible, and they certainly can't support the consumer base that makes the robber baron's company viable.
The perfect tax haven would be something like what CyberYugoslavia will be if they ever get their 20 square meters and UN recognition. No expenses but server space. There is no way a non-virtual country can compete.