Fizzle - That's so funny, I was just about to post the exact same thing! I've gotten my Big Shot out and started cutting some fabric experiments, and it's working really well. I happen to have the original set of purple Sizzix dies that were designed for quilting (many years ago). Now they make the "Fabi" dies which are specifically fabric-oriented shapes.
I also have an Accuquilt Go, and supposedly those dies can be used in the Big Shot with a shim. I haven't tried that yet, but I will soon.
The reason I dragged the Big Shot out again was not even to cut fabric, actually. I discovered the new Fat Quarter Wrap die from Sizzix... you use it to cut poster board or comic book boards, and then the FQ's wrap exactly on the board and are held securely. It's designed for them to be stored in a photo box and is a really interesting concept. I will also have to come back and post photos of my FQ's all stored neatly, for a change, not in a jumbled pile somewhere in my sewing room!