Anyway, strangely enough it's not the DX10 that will make Crysis not work on the consoles since the game will work on 7800GT/X1800 onwards, but more about how the entire system is put together.
on PC's you can easily have a 1GB RAM requirement, this is not wise on consoles at all. Despite the large bandwidth between the individual components, the ram to hold all the game data just isn't there. On the XBOX360 you're sharing 512MB or ram for the entire system, yes the EDRAM is hella useful and is amongst the greatest things on the 360, but it's only 10MiB.
This 10MiB also holds full frame data, that is a full back and front buffer image sometimes, but other times is filled with a single frame and it's sampling data (480/576p with 4xAA 720p with 2xAA or 1080i with no AA) and you can't use this to store game textures.
On the PC however, yes texturing from ram is slow, but you can if you have too with at least 5GB/sec available, but more than anything the actual game content can reside in the ram without having to stream from HD which brings you right down to the 60MiB/sec mark
And every PC has a hard drive, that is not the same for the console. The 360 core having no storage media (not counting removable drives etc...) would mean streaming large volumes of data straight to the system ram from the optical drive which is even slower than the disk at 20MiB/sec at most in the case of sequential reads, should you have to do jumps that would get even worse.
Clearly not feasible for the Console :/ Not related to the API directly, but just an example of why somethings don't make sense on console esp next gen stuff.