Yeah, but that kinda is trying to find the right data to make the theory work, right?

The usefulness of your loss, to me, is measuring how uncertain the data is. If you grow this to a multi-dimensional problem in which there is no easy way to measure this by hand, your regression network might be thought of as a non-linear noise measurement tool. What I don't know is if it would backfire for more complex tasks (such as outputting a nearly constant uncertinty)