Washing is for checking for dye ooze, but drying in the dryer does the shrinking if it's going to shrink. You'd be surprised at how many fabrics actually shrink. Real batiks never shrink because of the batik process, but they can ooze dye. If I'm making a wall hanging, I don't bother with either. But I usually don't know that when I buy a fabric.
Cutting corners hasn't always worked for me, so I serge cut edges before washing. It's fast and sure.