Most of the side quests serve the same purpose as the MSQ's - they flesh out the game world and reveal important lore and events. You can make the argument that some side story content such as Hildibrand exists in a little bubble of its own but beyond that...
The Warring Triad quests are tied heavily to the MSQ's. A lot of minor side quests only open up after completing certain milestones within the MSQ's too. Some of them are very in-depth, too, revealing a lot of stuff about a particular area or telling a story that fleshes out specific characters to a decent extent.
I feel like it does a disservice to the development team to act like they're irrelevant or not necessarily canon. FATE's, too, reveal a lot of interesting lore that serves to flesh out the game world. We learn about what sort of threats plague a particular region, the habits of specific types of monsters and so on.
It's also very unfortunate to see posts pushing blatant headcanon so heavily upvoted within this thread. Though I suppose that only serves to cement my belief that a handful of the regulars here aren't interested in the canon lore so much as their own personal interpretation of it. Surprisingly, I see more in-depth and nuanced discussions surrounding lore on the FF14 Reddit and general discussion sub-forum these days.