ASML is also part-owned by their customers. Intel, Samsung and TSMC all invested in ASML to get EUV tech over the line - see aforementioned capital requirements.
This could, theoretically, change at any moment, and Canon is trying something with their new generation of nano-print tech.
So till ASML starts abusing the position they should be good legally.
But no worries: in a democracy we expect ordinary people to have some interest in the laws, after all, they are supposed to be electing people who decide on how laws should be changed (or not). So layman need to talk about laws, too.
I'm just always a bit cautious (or at least I should be). I know that eg in the US insider trading is about stealing secret from your employer; but in eg France insider trading is about having an unfair advantage over the public.
I can image that there are jurisdictions that treat monopolies by themselves as a problem. (Perhaps France, again?)
Btw, for the US herself have a look at https://fee.org/articles/the-myth-that-standard-oil-was-a-pr... to see how the prototypical case against Standard Oil wasn't really about monopoly abuse, either. At least no one really bothered proving that a monopoly was abused, they mostly just assumed it.
> Antitrust is not against monopoly, but monopoly "abuse".
So this might be true about anti-trust in the US right now. But I'm not sure whether it's true about ant-trust law in eg France?
Also, in practice this was not true about anti-trust law in the US historically: Standard Oil was smashed into pieces without anyone proving in court that consumers had been harmed, or that the monopoly had been 'abused'.
See eg https://fee.org/articles/the-myth-that-standard-oil-was-a-pr... and https://www.econlib.org/library/Enc/Antitrust.html
So, as long as it treats fabs in Europe fairly, it can do whatever it wants in the rest of the world.
[1] https://en.wikipedia.org/wiki/European_Union_competition_law
ASML is a strategic asset.