Why isn't the index a tree?

I expected the index to be implemented something like a ref to a tree object (per stage) plus some stat()/assume-unchanged/etc. metadata. Instead, it appears to be a (sorted?) flat list of full paths with their associated SHA1s and metadata.

Is there a reason why each stage in the index isn't implemented as a tree?

If the index was a tree, I believe it would make several tasks easier:
   * you could easily get the diff between stage 1 and some arbitrary 
revision (e.g., git diff HEAD^^ :1:)
   * you could commit and checkout empty directories
   * you could use update-index --cacheinfo to directly insert/replace 
an entire subdirectory
   * etc.

Thanks, Richard