Publishing thesis as a book
Definitely don't print it before achieving your degree, in case you have to make major corrections (in which case the book would be a wasted expense).

In the UK, at least, it's usual for the final copy of a PhD thesis to be bound as a book - so in some respects, what you say about "ready to go to the print shop immediately" is already surpassed. However, that is not to say that the internal format of the work is that which would be expected for a normal book, and I imagine that this --- as well as perhaps writing to be accessible to a slightly wider audience --- is what is normally involved with somebody publishing their humanities thesis in book form.

The question that you perhaps need to ask yourself (or better explain to us) is: Why do you want to do this?