Iodine is not a strong oxidizer for getting rid of organics (bather waste). So it needs to be looked at in the same way as N2 -- that is, as a sanitizer, but not an oxidizer. So it would be used in conjunction with a non-chlorine shock (MPS) or with chlorine which would oxidize bather waste and re-activate the iodine as it got used up. Additionally, it isn't used in pools because it doesn't kill algae and in sufficient quantities to be effective it gives the water a slightly green color. It's more commonly used for personal (i.e. camping) drinking water disinfection, though its taste is objectionable so other products are typically used (such as a combination of Dichlor and sodium chlorite to produce chlorine dioxide).
Basically, if someone wanted alternative persistent sanitation, N2 would be a better way to go. You'd still need either MPS or chlorine.