Honestly, this whole conquer and oppress thing that Garleamald has going for it started out as them trying to put a lock down on the summoning of primals. So in essence they were trying to save hydaelyn.
It didn't though. This is a common misconception - Garlemald's conquest has nothing to do with the Primals, other than that the Primals are in the way. Their entire opposition to them is that Othard summoned theirs when Garlemald tried to invade, it cost Garlemald dearly, and Garlemald would really rather avoid similar losses in taking Eorzea. That suppressing Primals is pretty good for Hydaelyn is completely coincidental.