But there's a good chance that the world would be more productive as a whole. Governments typically trade economic productivity (by increasing friction) for ostensible social benefits (via tax-funded programs). Of course, it's not clear if this tradeoff always works out, because governments may spend sub-optimally or divert funds towards things like war.
Governments often increase productivity. Try investing in a country with no laws, education, or infrastructure. They can also help make an economy more efficient by maximizing positive externalities and minimizing negative ones. Social benefits can also be beneficial economically as an externality. Companies don't have the incentive to keep someone from starving or to educate them from kindergarten, but having a larger, more educated work force certainly benefits the economy as a whole.
Has "eventually" happened yet? US tax policy has gotten worse in recent years; give it some time.
>Instead, it's companies in higher tax countries that are the largest.
The biggest companies are in the US, which is a huge country with lots of historical capital. There are hundreds of reasons big companies tend to be here, and you haven't demonstrated that excessive taxes are one of them.
Interestingly, many young tech companies like Google have their EU HQs (and sometimes global HQs) in Ireland for tax reasons.