Shout out to u/I_Am_Your_Daddy_ for posting the question in archaeology originally, but I'm very interested in this as well and there are no answers there!
http://www.gigalresearch.com/uk/publications-sphinx-secret-2.php
To sum up, Baraize was simply too busy to document. Why nobody has explored it, too dangerous to excavate until they can reinforce what's reinforced in the Sphinx more efficiently.