The problem is, due to what I guess is something of a flaw in the central idea, you ultimately have to provide the password for your inner volume when you do all of these things which don't involve it. So now your private data is split up over two drives, which is at least somewhat questionable, and also the "mundane" drive requires the "important" password.
This may be acceptable if you're collecting a small cache of text documents which you believe could harm a corporation -- then you say "no, I don't have those articles, see, this really is just my porn stash, please don't hurt me. But a criminal or a government -- no, they're willing to be patient and they're perhaps willing to peek at your password input prompts with webcams or audio-recordings. They would know that there's an extra password being entered every time you decrypt that file.