Just my 2 cents on the topic of SF4, while it is the best 3D game so far at adapting 2D style, and I like the non photorealistic 3D graphics, it just definitely does not play like a true hand drawn 2D pixel art fighter and this is because 3D graphics can't really translate many of the mechanics of real 2D graphic games.
A 2D game has more profound properties than just the visual aspect of being on a 2D plane.
It has more than the visual aspect of a 2d plane. When the game was first being made all the hitbox data had 3d properties. They changed this before release and the game's data all runs as if it's a 2d game. Idk that the game doesn't play like a 2d fighter, to me it seems no different from Blazblue/Guilty Gear in that aspect. For now I'm disagreeing with you but I'm not entirely sure I touched on what you meant.
Maybe I haven't payed enough attention but the games detection and 2d aspects never seemed much different from Third Strike. Though definitely far from the KoF games but no Street Fighter is very relate-able to those.
And on the topic of SFIV being 3d or 2d, I don't think that you can't definitively say either. Really it comes down to what you define as a 2d/3d fighter. To me if you can't side step it's 2d. You couldn't side step in Fatal Fury, you could switch planes. It's not the graphics that determine it for me, it's the gameplay.