I did a landscape quilt using a straight stitch with clear thread close to the edge. I still got some fray, and I'm using batiks.
For mine the little big of fray doesn't bother me too much because it's a landscape quilt - so it kind of has that "nature" look to it. Had I done an applique like Eddie's gorgeous William Morris pictured above - the straight stitch method that I used would have ruined it.
So I guess it depends on the overall "look" that you want.