It's equally convenient, since the mean doesn't care about the shape. I don't think it's particularly jarring - just imagine it going to 0 at the edges.

The reason you'll probably end up with something like a bell curve is a practical one - the central limit theorem. For complicated problems, you very often get what looks something like a bell curve. Hardly watertight, but I'd bet decent amounts of money that it is true in this case, so why not use it to add a little color to the description?