I don't know about serging the edges, I really like the double folded french binding cut on the bias, machine stitched to the front and hand stitched down on the back. I've tried other finishes but keep coming back to what I refer to as "competition" bindings.
But I do often stabilize the edges, especially with heavily pieced borders with a row of stitching within the seam line and I think the serger would do fine with something like that.
I have known quilters who serge their seams, especially with projects like the jelly roll race.
Despite what the quilt police may think, there are no rules (except in competitions).