I understand how linacs and even small compact syncrotrons can have practical medical and industrial applications, and I understand that in the past CERN has developed technology and produced research which is relevant to hardon therapy.

What I don't understand, and maybe you can clarify, is how the very largest gargantuan accelerators can ever have practical relevance. How can effects and products which can only be studied with accelerators that are many miles large ever have application in hospitals unless those hospitals are also many miles large? Not going to lie, I get "NASA invented Tang" vibes whenever this subject comes up; like the medical applications of small accelerators are obvious and parsable to the public, so they are used to sell the public on accelerators the size of small countries.

Because of the engineering effort required to build such systems, that no one has built before, means there is a gigantic amount of R&D discoveries that can be eventually applied in other fields outside particle physics.

Mechanical, electronic, informatics, chemistry, physics,...

Hence why CERN eventually created an industry collaboration office, responsible for finding business partners that would like to make a business out of such discoveries.

https://knowledgetransfer.web.cern.ch/activities-services/co...