Hello! I don't know if you (or others) are still having this issue, but I recently ran into the same problem myself. To be specific, this happened with the Iron Bull romance cutscene that culminates his romance path. The scene would play entirely fine, save for these intermittent black screens wherein the subtitles and dialogue wheel would still appear. This is the only cutscene that had this issue; everything else in the game played fine, and lowering the graphics settings did not help. My graphics card drivers were all up-to-date as well.
However, after trying out several things, I found what may be the issue. If your bed is set to one that has a high back, large bed posts, or other such obstructions (I was using the Free Marches II bed), this could be obstructing the camera. I set my bed back to the first one you get (the Free Marches bed), and this fixed the issue. No black screens at all!
So, if you (or others) are still having this issue, I would suggest trying this possible solution. Hope this helps!