EUV is truly amazing in that it works at all. The shot noise is simple to fix in theory - just get more photons. In practice, it's going to be really challenging to get more light out of the molten tin droplets.
I did an internship for one of the two big lithography optics companies back in 2005 in their R&D. Their engineers and scientists working on EUV were very cynical about the EUV prospects. Some of that will have been because switching from tech you understand (lenses) to something you don't (mirrors). But wow, did they NOT think that was going to work.