The actual valuable technology is the EUV light source tech developed in California by an American company that ASML acquired in 2013 under a strict technology export agreement with the US government. It was not developed in Europe.
The light source tech was pivotal, but the supply chain mastery of 100,000 parts and patience to invest "200 billion dollars" in development over decades is deserves massive respect for the Europeans, no? This effort did not start in 2013.
The technology itself is researched and developed in San Diego. ASML in the Netherlands is just the assembler of the final machines. That's not the particularly valuable part of the product pipeline.