Why aren't we going electron lithography? As a laymen I think it should easily be able to surpass EUV in terms of resolution. I would imagine there are very good reasons why we aren't seeing it.
When the choice was made to go for EUV, E-Beam was actually the most mature technology available for next-gen lithography - but it just wasn't economically viable. The technology has remained in development over the years, but not a lot has changed yet.
If you want to know more about the topic, I can strongly recommend this video from Asianometry: https://www.youtube.com/watch?v=RmgkV83OhHA
It does highlight some potential pitfalls. Chiefly the rapid decay of muons and dealing decay particles. Also you need a source of high energy protons.
Proton lithograhy anyone?