Everything was a challenge with EUV—the source, the vacuum, the mirrors, the reflective reticle, getting sufficient throughput…
Alternatives were tried. Synchrotron EUV sources. (works, but huge). Linear accelerators (The SLAC beamline was used as a light source as a test). X-ray lasers (don't work yet). Electron beam lithography (works, but too slow.)
There's got to be a better way to do this.
EUV masks are made that way, slowly.