> Perhaps in theory, but many countries around the world and across history (including the United States!) have had much more progressive taxation regimes and it hasn't "kill[ed] the incentive for starting companies and becoming wealthy."

Which countries? And what happens when another country becomes more competitive than the US from a tax perspective? Will it destroy the country? certainly not. Will the US continue to be the world reserve currency and lead the world? Again, no.

The United States had very high income taxes from 1950 until 1980 (and also grew very fast during that period - much faster than in the period 1980-present). It is also worth noting that the United States was actually the leading advocate of very progressive income taxes during that period - convincing many other countries to adopt extremely high top tax rates on the wealthy. Today, most developed countries have higher top tax rates (and more progressive tax regimes) than the United States does - Germany, France, Sweden, Japan, etc. etc.

> And what happens when another country becomes more competitive than the US from a tax perspective?

This is a really important point and I'm glad you brought it up. The progressive taxation regime has been undermined over the past 30-40 years by the "Washington consensus" - the idea that free flows of goods and capital are paramount and that it should be US policy (as well as the policy of the IMF, World Bank, etc.) to pursue such ends via trade agreements and in exchange for loans. The issue is that free flows of capital leads to the exact problem you describe: a global race to the bottom on tax rates and a general nihilism about the possibility of an equitable tax regime. The long term challenge, then, is about building transnational agreements that are about more than just free flows of goods and capital: they must address issues of taxation as well.