I'm going to stop you there. Sure, I could argue with the whole of your post, but my arguments has been 'Done there. Everyone knows my arguments'. So all I'm going to say is that KH2 is terrible story-wise.
But darker and edgier? Kingdom Hearts 1 was darker. I wouldn't say it was edgier (seriously, how is edgier a term for 'better story'. it makes it sound vain and trying too hard), but it certainly was darker.
Let's see. Kingdom Hearts started out with a CG cutscenes of Sora not reaching his friend and always falling through the ground, ocean, whatever. Then we have him in a dream tutorial where there is nothingness, where there is a music playing that could be fitting for a mysterious atmosphere. The fact that the shadow comes out as well as the 'weird questions' that Tidus, Wakka and Selphie asked you (making you think about 'life') and that's without pointing out about the Darkside that tries to kill Sora or try to drown him in Darkness.
There is a reason why Kingdom Hearts 1 had a spider for a PEGI rating (indicate fear). It is actually dark when it came to cryptic messages and that the design of that 'tutorial', Hollow Bastion's castle and The End of the World were quite scary. In that regard, it is a lot more darker than say, Kingdom Hearts II's supposed moral grey area of Organization XIII (which was a huge downgrade from COM) or Sora forced to kill Heartless to benefit the Org, otherwise lives could be lost.
(And the latter on Sora forced to kill Heartless. It didn't really feel like something that hit me. It could be the bad writing, but there weren't any consequences or story impact)