According to the article if they make it 100 times more powerful it would be useful for producing radioisotopes for PET scans, protons for proton therapy, heavy ions for heavy ion therapy, etc. Currently the particle accelerators used in medical facilities are big and expensive so this would make them far more accessible to hospitals world wide.
Why would it not work?
For avoidance of doubt, I'm not imagining a miniature device, just possibly a linear device that is maybe smaller than LHC. They used to use linear arrays prior to development of synchro-cyclotrons, IIRC.
Seems like it would be somewhat akin to a beam of single particle light-sails.
Basically, I was imagining this - https://www.sciencedaily.com/releases/2023/07/230731110723.h... "New method improves proton acceleration with high power laser".
All my best ideas have already been done!
IIRC, from earlier reports and articles, this will be more useful for biology and chemistry, and perhaps not necessarily for the kind of experimental physics being performed at the LHC.