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.