The article referenced mentions of goitre in Switzerland from Victor Hugo in 1839, Mark Twain in 1880, a medical survey in 1883, and Roman authors like Vitrivius and Pliny the Elder. It also mentioned that the iodine idea had been going around for a hundred years before the activities of the heroes of our story.
Iodine had not been seen as a successful cure before because excess iodine causes a horrible condition. The key difference here was that Hunziker proposed regular use in minute quantities, and then Bayard tested the hypothesis with careful measurements and convincing evidence.