I save reasonably large pieces of batting. I use them to practice FMQ and also to check if things are set up right before working on my project. By that I mean, I make a small quilt sandwich and stitch a line or so to see if the tension is right, etc. And invariably, I'm doing a small project and want to have a small piece of batting. And they can also be used as stuffing in some projects.
As for stretching the back, I did that the first time I did FMQ and everything worked fine. But then I read the same tip, and so never did it again. I didn't notice a difference, except that it was easier to make the quilt sandwich if I didn't bother pulling the thing taut.