The ringworm fungus itself is not so difficult to kill with chlorine. As noted in
this old 1933 paper, 0.4 ppm FC in swimming pool water (that would be without CYA in those days) effectively did a complete kill in around 2 hours. Our pools with the minimum FC/CYA ratio have an equivalent FC with no CYA of at least 0.06 ppm in non-SWCG pools so that would be a complete kill in around 13 hours. At SLAM levels that are equivalent to around 0.3 ppm FC with no CYA, the complete kill would be in under 3 hours. So a SLAM is the reasonable thing to do.
However, it's the spores that are more difficult and these are more like other spores or oocysts that are more resistant to chlorine. The test described above used scrapings of live active fungus from a patient and while that is the most likely mode of transmission in a swimming pool, it is also possible for spores to be transmitted and the experimental procedures they used for culturing may not have activated spores (i.e. it was more for testing the viability of live fungus). However, unlike the protozoan oocyst
Cryptosporidium parvum where the infectious dose is around 10 oocysts (see
this link), exposure to dermatophyte spores does not always lead to infection (see
this fact sheet). The infectious dose for some foot fungus is on the order of 280 for half the people to get infected (see
this link). So water dilution will likely prevent transmission of this disease if only one infected individual were using the pool.
If one wanted to ensure getting rid of spores or oocysts from a pool, one could use chlorine dioxide, but that's not a normal procedure and should really be something reserved for emergency handling of a diarrheal release thought to contain
Cryptosporidium parvum.
This chapter in a book goes into a lot of detail on skin fungus infections including ringworm. The pictures with extreme cases are pretty awful.