The US cant block a european company from doing anything
They can, since ASML are using US technology. Especially after ASML brought out Cymer.
If I recall properly, and if I trust what I read/viewed from the internet ages ago, EUV optics is from Germany (zeiss), and the EUV light is from cymer. cymer almost lost their part because they had been unable to deliver enough EUV light power for too long (in the end, it seems they shine their massive CO2 laser on a tin droplet, 2 times instead of one and yield enough power). mask/wafer alignment equipment, dunno where they are from (nanometric piezo-electric motors, with probably laser interferometer). Then, at the time everything was run in extreme vaccum, but heard something about hydrogen gas.
The US cant block a european company from doing anything
You think ASML wants to run afoul with the US, even if they can't force ASML? The main reason ASML has EUV is because it was funded by the US government to develop it. Now the tech is mostly ASMLs own, but they still have close ties to the US. USA didn't have to force ASML to stop selling to China, they just had to ask them nicely.
The company (originally named ASM Lithography, current name ASML, which is an official name and not an abbreviation)[10] was founded in 1984 as a joint venture between the Dutch companies Advanced Semiconductor Materials International (ASMI) and Philips.
There is a positive feedback loop in fab progress: the more customers you have the more yield experiments you can do, the better the yields get, the more customers you get. This explains why the number of leading edge fabs is decreasing, ending up with a monopoly:
The Chinese government wants it to happen and probably can make it happen, but it will not be easy. China would have to take the island by force and an amphibious invasion is logistically difficult and almost certain to face heavy casualties on both sides.
US and the west place a lot of strategic importance in Taiwan so they may come to the defense, but it is unlikely to be defendable for long.
We are seemingly moving towards another Cold War: China and Russia vs US and NATO.