The most technologically critical component of ASML's EUV lithography machines (the EUV light source) is designed, developed, and manufactured in California by Cymer.

And another extremely critical piece of technology is the mirror from Zeiss, which is not manufactured in the US.

Yep, absolutely true. ASML is a critical technology provider that both the US and EU are dependent on each other to maintain.

And the US does not need ASML. Europe could use ASML, but doesn't.

The US doesn't need ASML.

Right, ASML is so replaceable that the US forces the Dutch government to put export controls on some of their machines.

There's no substitute in the world for the top tier machines ASML makes.

> forces the Dutch government to put export controls on some of their machines

That's because the critical EUV light source technology is developed in California by a US-based subsidiary of ASML. The US and EU have mutual interest in protecting the technology and machines. If export control agreements were not in place then ASML would have never been permitted to acquire Cymer. And if they are not enforced then the US would almost certainly require ASML to sell Cymer back to US ownership, TikTok-style.