USA didn't have to force ASML to stop selling to China, they just had to ask them nicely.
That seems like 20% true. The US had a brief EUV program ("EUV LLC") in the late 90s - it wasn't much compared to how much difficult, risky, and expensive development obviously still needed to be done afterwards. The EU also has basic semiconductor research, notably IMEC.
I have also seen that claim in a YouTube video by "Asianometry" and I wonder what the original source of that apparent misinformation is.
But USA didn't have to force them. ASML's EUV tech started out as a US funded venture, so I don't think they want to start a fight with USA.
And USA could obviously change its laws to block sales of technology even if less than 25% of the end product is from USA.
Think back to what went on from 1950-1990 in Europe and Asia, except it'll be even worse.
Blocking Nordstream 2 is the very bottom of the barrel compared to what's coming.
After a brief slumber the Russian Empire has awoken again in Europe and it's annexing territory (again). The Dutch would be foolish to spar with the US over ASML at this juncture. Dealing with Russia in Europe and China in Asia will take a concerted front by the US, Europe and their allies.
There's a reason PRC has much more success poaching TSMC employees than US trying to fill up new fabs. Why TW has drafted laws to prevent TW semiconductor talent from working on mainland. Generally TWers prefer working in PRC, with comparable language / culture. Great compensation and quick flight home. Reality is most of TSMC employees will been prevented from being paperclipped to the US in event of war, their future will be firmly tied to PRC and as significant assets, they'll be treated with more carrots than sticks.
But it'd still lead to a massive global chip shortage if TSMC's facilities in Taiwan were wiped out. And I guess that is a deterrent that Taiwan can use against China.