Potential spoilers ahead.

Have you been through the Twinning and all of the main scenario quests? Then you know Cid helped deal with Alexander and Omega with or without the Warrior of Light, and his vision made it possible for scientists after him to manage inter-Shard travel. Therefore, while not part of the main scenario quests, the events surrounding Alexander and Omega are canon. If you're a summoner, it's pretty clear the events surrounding the Binding Coil of Bahamut are also canon, even if you personally hadn't bothered.

So what's the big difference between Eden being side quests instead of main scenario quests?