Indirect mode repos can be cloned over http, and just work. But, direct mode repos don't currently work; while git can clone them ok, git-annex get doesn't know where to get the file contents from.
To support this, git-annex would have to check if the remote is in direct mode, and when it is, it would need to download the direct mode mapping file, to find out which file has the content of a key. Then, after downloading the a file, it would need to make sure to checksum it, since nothing prevents a direct mode file from being modified at the same time it's downloaded.
All seems doable. However.. caching database wants to switch the direct mode mapping files from simple flat text files to a sqlite database. Which would complicate this a lot. Can sqlite databases be accessed over http, or would the whole, possibly large database need to be downloaded? If so, what to do when the database changes? Re-downloading a possibly large db is not good.
Alternatively, the direct mode mapping files of the remote could be bypassed. Instead, look at what the remote HEAD branch is, and look at that branch locally. Create local direct mode mappings for the remote HEAD branch, and use them when downloading.
This approach would mean that, if the remote's HEAD changes and we haven't noticed, we might download the wrong file (that has eg, been moved). checksumming would detect this, but it does make it more fragile.
Also, creating the direct mode mappings for a remote HEAD would currently be pretty slow. Probably implementing the caching database for direct mode mappings would lead to faster code. So, this feature seems best blocked on the direct mode database either way!