I encourage you to take a step back and think about how landscape design is about creating space. We create the space first (the lawn or patio, for instance), then use the plants to reinforce that space. You can read more about this idea in my Keep it Positive in the Garden post. The bedline is the edge of that space, so it needs to be purposeful to reinforce whatever shape you are creating for the lawn or patio.
Catherine from Garden Drum has a great way to think about this concept. She describes the garden space we are creating as the doughnut hole, while the actual doughnut is the planting bed reinforcing it. The bedline would be the outer edge of the doughnut hole.
There is another benefit to stronger bedlines...less maintenance and easier mowing. Imaging trying to edge all those wiggly curves with a spade, or worse, trying to mow into those tight little crevices. Eek.