It works to shade the area, but is it original? The reason I ask is something like this usually had strips of wood running across it. I just wonder if it was put up there because the beams might not support the additional weight, or if it was just a cheaper alternative.

Check with a contractor to see what your options are.

That looks like a tremendous amount of weight for the support structure. I would examine that first. Looks like it could fall down and those timbers are big and heavy. Start with that. There are fabric solutions that you can move along cables that could help with debris removal, etc. But we are talking about a significant investment for that large an area. No matter what you do, without an angled decline from the house toward the pool, nothing is going to be easy. Safety first, however. Have that structure inspected.

Personally I haven't met a structure that doesn't benefit from lighting I would just do something fantastic with my lighting like chandeliers something unexpected to balance the heaviness of the beams but add to the softness of the fabric you really just need to soften all of that heaviness also I would run some Vines up there make sure that it's something that's not going to take your roof off to your house but something to soften your edges hope it helps enjoy your lovely pool

What happens when it rains?