Yes but the point is that if their main HQ is in another European country they can't avail of the repatriation laws unless that country has similar laws. Of course many EU countries have lower corporate tax levels than the headline US tax rate, but not all. I'm more concerned though about the race to the bottom in terms of corporate taxation than any EU/US competition. Interesting discussion, thanks.

No, because Google isn't paying the Irish corporate tax but instead moving the money to a second Irish company (hence the double Irish) based in the Bahamas. A European company with a subsidiary based in the Bahamas would trigger anti-avoidance laws, which a US company won't (until they bring the money back into the US) because of a loophole in the US anti-avoidance laws.

I think you misunderstand. The whole premise here is that none of the principals care where you're incorporated.

A company whose primary employees are in Europe and whose primary customers are in Europe can still be incorporated in Delaware and traded on the NYSE. These tax avoidance mechanisms aren't for "US companies," they only work if you're in practice an international company. A "European company" which is also in practice an international company could do the same by becoming nominally a "US company" without changing anything of consequence about their operations. Because international companies don't really care where they're incorporated.

The trade war isn't between US companies and European companies, it's between companies big enough to be "international" and everybody else.