I have an ironing surface that I made for my ironing board and didn't quilt it for the reason you gave. Since mine is just a rectangle board that gives across an open drawer, I could just make it pillowcase style which keeps it taut. I iron a fresh piece of white freezer paper onto it when the old one gets dirty. I think if you use elastic or string to make the sections taut on your ironing surface, it should not need quilting.