I'm currently working on a long-form article about numbers stations: why they're still utilized by governments because of their remarkably simple yet effective communication capabilities
They're still used 'cause they can't be decrypted by anyone who doesn't have the one-time pad, or "key".
2600 magazine had a good article on the maths of why this is so in the mid-2010's.
and why shortwave radio enthusiasts are eager to track a mystery that may never be solved.
Um... A lot (i.e. tons) of people have speculated for decades, for example going back to Havana Moon and H. Helms (both wrote books in 1980's) and many others, and by this point in the present, people at places like the old A.C.E. and this forum and N&O and Priyom (international but also .ru-zone) and Enigma 2000 basically "solved" the general topic and lately most of the specifics also. Not "the mystery"... every station, and even some transmissions themselves are different mysteries. New ones pop up too, the subject is fluid. The more things change, the more they are not the same any more.
Maybe what you mean is, no SWLer will ever be able to understand or decode a message, which is a fact. it's not possible (which again answers your first question)...
To answer the question "why", maybe because it's fun? It definitely beats watching the paint dry or reading an anonymous twitter feed. Don't knock it 'till yer tried it.