"Elbow Up" is not an absolute. Many hitters keep their elbow up because that's the way they were taught. Many coaches taught to keep the back elbow up because if the back elbow stays up, the hands stay up. Where the hands reside is much more important than the back elbow being in the up position.
My personal experience says that the back elbow impacts the path of the hands. When playing slow-pitch, I raise my back elbow when I want to stay on top of the ball. If I want a fly ball, my back elbow goes down a bit. Initially, my DD's stance had the back elbow up. Over the last couple of years, I've dropped her elbow, with more well hit OF shots as a result.