I would have hated it if Nanaki's backstory was purely Shinra related. Everything is Shinra related. It feels trite. Nanaki a reason to fight them, which is good -- that's what brings the party together after all -- but to have Seto turned to stone defending from Shinra or something would've just been stupid. Like, "yes okay Square we get it Shinra is bad".
Going to Cosmo Canyon gives you the insight into Nanaki's character and it also makes dealing with stuff like the key to the ancients and whatever less of a deus ex machina. Instead of Nanaki going "oh hey I know just the dude to help us out", we already know Bugenhagen might be helpful.
Besides: Nanaki said he wasn't interested in sticking around. He was going as far as his home village and then leaving. You might not have it now, but the first time I played I was fearful that he would leave my party.