If I remember correctly it's a driver limitation, and theoretically it could be modified so it would do what you want, but consider the amount of userspace/kernelspace crossings to be made just to send some ciphertext over the network to some other party.
I imagine something like this would take place:
SSL does not happen in the kernel. So you need to send a payload to the kernel to encrypt, you get back the ciphertext, wrap it in your packet (add some headers) and then push this data once more to the kernel, which sends it out over the network for you.
Receiving ciphertext would go along similar lines.
That's probably not very efficient. Contrast this with full disk encryption using dm_crypt (linux). No shuffling back and forth of data. Userspace only really needs to handle the plaintext (and not even directly, but through the FS layer, which is also in the kernel).
So maybe it may just not be worthwile to expose the interface to userspace on reasonably powerful platforms? Anything above a tiny MIPS or old 486?
The VIA padlock crypto accelerator is (or was at some point) exposed to userspace and OpenSSL could take advantage of it. I wonder how much of a performance increase that yielded, considering the issue I noted above.
Also, hardware accelerators typically only support a couple of modes and key sizes. That's fine for full disk encryption, but in a networked world you need more flexibility.