Jyggalag is a ridiculous entity. I loath SI.
IMO, Jyggalag makes perfect sense symbolically. See, true madness must contain a shard of sanity. Because when you can't even rely on a madman to be mad is when things really start getting interesting. And by the same token,
if Jyggalag as we met him in SI
did truly separate from the ascendant Hero, it does not mean that the 'new' Sheogorath will not be subject to the 'same' cycle. For if the ascendant Hero truly embodies madness, a shard of sanity will by necessity crystallize and begin the whole thing again.
From another perspective, you could say that Jyggalag himself is purely insane. 'Cause, really, pure logic's insanity, and particularly the way that he does it. Which I feel is reflected in his long-gone Library's fallibility.