Why would X Ray film have emulsion on both sides? Shouldn't single side work fine for X Rays?
First, keep in mind x-ray film doesn't really record x-rays. It can And it would, but in a typical medical setting the flux is way too small to generate an image. Instead, the x-rays hit a phosphor screen which emits visible light, and that is what creates the image.
As to the double sided nature: I suspect it's because it's basically "free" additional density for the same number of photons and thus the same x-ray dose. Which means less exposure to the patient for the same image density, do less risk of tissue/dna damage. Ease of use might also have something to do with it as there's no risk of loading the film in the wrong orientation in the exposure unit.
Apparently applications like mammography require higher resolving power or better/higher fidelity rendering of very fine structures. For this purpose a single-sided film is apparently preferable because it can better deal with scatter, halation etc. which would erode this fine detail.