Good fabric still looks and feels good after it is washed - if it didn't there would be no point in making quilts. I use starch while I'm quilting, and I want it gone before I gift a quilt. Many people have smokers, cats, dogs, or other critters in their homes while they are quilting, and the recipient may have allergies. I can't think of a single reason why a quilt shouldn't be washed when it is gifted, even if the fabric was pre-washed.
I put most quilts in the dryer under low heat and take them out when they're still just a little damp. I then lay them on a clean surface (e.g. a sheet on the floor) for blocking, if that's necessary.