1.   French runners are basically strips of very hard, solid wood attached to the bottoms of the drawer sides.

2.   If they are still sticking, plane the tops of the drawer sides.

3.   It would be cheaper and less of an atrocity to buy pre-cut drawer sides in plywood.

4.   Nobody is daft enough to veneer drawer sides.

5.   Some drawers have one-piece fronts that are glued to the drawer sides and are not removable.