One problem is that it's turtles all the way down.

What's your confidence in your confidence probability estimate? You can represent that as another probability distribution (or another model, or a set of models). Rinse and repeat.

Another problem is that it's hard to get reasonable estimates for all the curves that you want to mathematically manipulate. Of course you can wave hands and say that a particular curve exactly represents your beliefs and no one can say it ain't so, but fake precision isn't exactly useful.