Nikon actually supplied the machines for Intel through their 10nm debacle. Canon has completely retired into the low end market, but used to be massive. You're right that I forgot about Applied Materials.

I think historically it's been a challenge mostly related to precision optics, given that semi production is more or less like exposing photographic paper from a negative, through a lens using a light source.

With EUV the challenge is the crazy difficulty of generating the required light source at the right intensity and focusing it. At that wavelength things behave differently, to say the least.