Post processing algorithms can't deal with sub-pixel aliasing problems properly, there's still a place for MSAA, particularly if you can implement it with an utterly trivial performance cost.
You're still doubling the number of pixels to fill and shade by rendering at 1080p. Being able to fit your whole framebuffer into super fast eDRAM will certainly help performance but its only one piece of the puzzle.
No, in such a situation, you'd simply employ tiling, like you do if you want MSAA in a HD X360 game. In reality, most developers will probably use a post-process AA for native 1080p games or even opt for something like 1280x1080p w/2xmsaa and a native 1080p HUD, as that would fit into the eDRAM just fine.
Just because you can fit a 1080p framebuffer in eDRAM, doesn't say anything of its complexity. It gets rid of one of the biggest obstacles to 3D graphics (bandwidth) but you're still left with ~2 million pixels to fill and shade.
If the eDRAM is more a general pool of memory (as I suspect it is) rather than the 360's scratch pad, then many developers will probably want to use that space for multiple other buffers, rendering at 1080p is going to ruin your chances of that.