That cusp isn't a failure, so much as the definition of parallel not matching your expectations. You can't have the radius of the curve smaller than your offse

That cusp isn't a failure, so much as the definition of parallel not matching your expectations. You can't have the radius of the curve smaller than your offset without forcing a cusp. If you imagine dragging an eraser across the 'roadway' produced by the parallel lines, you'll see that the solution with the cusp still obeys the constraint that the lines are a constant distance apart for every point along the road, it's just that it turns so tight your eraser needs to turn in place at the corner.