> Right now, it doesn't. But I don't think it is because they are OK with European companies dominating US market. It is rather because there are no European companies at the moment capable of dominating US market. The moment a company in Europe starts to gain significant market share from American companies in the US, the government would (most probably) step in and stop them.

Airbus is a great example of this, the US repeatedly cockblocks Airbus from making major US military sales, puts tariffs on them, etc.