the engineer is going to have considerably more work. also, you're (or should be) paying the musicians. not to mention all the prep work that would need to be in place so the songs are ready to record live. you might see a little bit of dollar savings but it comes with lots and lots of extra coordination and work.

the biggest thing to me is, and most obvious reason as to why we don't see more live albums, is that the artist may not want a live version! especially if you have any electronic or digital elements, those will hit very different live than in the studio.