The fusible washes away when your finished project is laundered- getting rid of the stiffness. I use heat n bond lite often, there is also misty fuse which is very lightweight.
ive only needed a stabilizer behind my blocks for stitching when I was using very thin fine fabrics ( silk and a lightweight batik) I generally use a small blanket stitch or zigzag. I don't do satin stitch ( personal choice, don't like the heaviness/ stiffness of it) when I have satin stitched I found I needed stabilizer.