The issue isn't in generating short wavelength light, it's in focusing it accurately enough to print a pattern with trillions of nanoscale features with few defects. We can't really use lenses since every material we could use is opaque to high energy photons so we need to use mirrors, which still absorb a lot of the light energy hitting them. Now this only explains why we need all the crazy stuff that asml puts in it's EUV machines to use near x-ray light, but not why they don't use x-ray or higher energy photons. I believe the answer to this is just that the mirrors they can use for EUV are unacceptably bad for anything higher, but I'm not sure