Consider this: Crystal-like-Law is destroyed, Altmer are desperate. Jyggalag is freed from Sheo around the same time the Thalmor are formed. Who is Jyggalag? Their Knight in CRYSTAL armor. Wink, wink. It would explain their extreme view on their corrupted version of true anuisim. Jyggalag is the extreme end of perfect order.

That and it gives Jyggalag solid involvement in the next TES

The whole Jyggalag-Sheogorath thing was a mirror image of Auri-El/Lorkhan.

Jyggalag represents Auri-El of Anui-El. Sheogorath represents Lorkhan of Sithis.

Jyggalag is the Crystal God. His Knights are crystal constructs, and they came from crystalline obelisks during the Greymarch. A lot of crystals there. Now take into consideration Crystal-Like-Law. A literal crystalline tower that housed all of the Aldmeri culture that kept the Altmer, well "pure" and true to their ways even in the harshest of times.

Oblivion crisis happens and the Daedra completely raze the tower to the ground. Around the same time, the Oblivion crisis ends, Jyggalag is freed. Thalmor are formed. Now I'm not saying they were Jyggy cultists at first... but they likely caught his attention(or he caught their attention) and thus a connection was made. The crystalline Daedra, hated by his Daedric brethren happens to be the one Daedra these crazy Altmer can relate with, and he also just so happens to represent crystals...

His sphere and methods no doubt seduced them, and they likely see him as their fallen champion renewed, or something along those lines. So now we have the Thalmor in full force 100 years later, trying to achieve their goal of perfect order and Stasis, which fits in nicely with Jyggy's sphere of order and cold logic.

Jyggalag could in theory, benefit from this. Mundus is chaos, and in mythology, men are the children of Lorkhan who is chaos. Destroying that and unbinding the Dragon would lead to permanent Stasis.

Assuming it all works of course, but I doubt we'll find out... Doesn't mean Jyggy and the Thalmor won't try. Or perhaps the Thalmor seek to use Jyygalag as a means. If the Thalmor are destined to fail then Jyggalag would predict this. So why go along with it? Jyggy is smarter than he looks. He like-wise sees the Thalmor as a means to his end. Through their vigorous worship and enactment of his sphere, he gains power from the whole ordeal. Whether the Thalmor fail or not is irrelevant to him. either way, he gains the necessary influence to manifest on Nirn the same way the other Principalities do. And now he can work on his obsession with Order on the Arena where it's fair game. Instead of pissing off the other Princes again.