Why is it a flawed analogy? The first things Lews Therin did after being healed is channel. Aes Sedai are addicted to the True Source, especially ones that live for hundreds of years such as in the AOL. Another reason men in the steddings left was because they couldn't stand not channeling. Not that they do it all the time, but it makes sense that a madman who's instantly sane will be fearful and will reach out for the Source.

We also know from the Ash'aman that some men go insane after a few touches of saidin. However, I would agree that this is generally not the case and that it takes months or years in most cases. That said, I do believe that because the taint is akin to Compulsion (as Nynaeve alludes), that someone who has been touched is much more sensitive to the next attack... As displayed by Liandrin when she uses her Compulsion on the shienarin noble in TGH. Therefore a man healed of the taint is sensitive to its effects, and thus the easy relapse.