Since originally writing this post, Evoto has come along and done just that: Letting you base all your shots on the crop of a single one. Works perfectly. In fact, if you're doing headshots or portraits, there's no need to open Lightroom at all. Evoto can shoot tethered, do a quick retouch on the fly (as the photo appears), and export. I'm not affiliated in any way with them, just impressed with how good they've gotten so quickly! Highly recommend.
Evoto is great, but for me that do school portraits I have to export the same picture in more formats and I use all keywords, face detection and color grading on the Lightroom. I don't do any massive edition beside that.
It would change my world to have an auto crop feature in LRC. I have played with a ton of different ones, and they either crop too loosely or don't respect the subject. I downloaded a trial of Capture One and their auto crop is nearly perfect. In their studio version, you can set percentages of border and have it crop for the subject. But because Capture One is not only expensive for that version, but also doesn't play nicely with LRC files, it is just far too complicated for my workflow. I love LRC and would like to stay with it. I have that I am having to look at other solutions. For reference, I shoot Dog Sports and have thousands of images to crop. Having something to simplify that step would save me incredible amounts of work.