Length of cooking time for stews and sauces
Sure, a few things happen (or, rather, continue to happen) after the first 10-15 minutes.

Spices continue to release their flavor. Not a big consideration for finely ground spices, but something like whole coriander, cracked black pepper, or cinnamon bark will definitely have more to give at that point.
Vegetables will continue to cook. More cell walls will break, softening the texture and releasing more flavor. Starches will break down into simpler carbohydrates, becoming sweeter. Various other compounds will break down as well.
Water will boil off, concentrating the flavor.
Flavors will diffuse in and out of the vegetables, making the broth taste more like the vegetables and the vegetables taste more like the spices.
On the bottom of the pot, the high temperature may lead to a small amount of caramelization or Maillard browning.

Whether those are important or not depends on what you're going for. Fresh, summery vegetable stews don't need to cook for long, and benefit from careful texture control, while a smooth, melty ragout can't be rushed. Often you'll cook some of the stew for hours, then toss in more ingredients scant minutes before serving.