If I remember correctly didn't XCOM use a still image for when you couldn't see something happening and then flashes of the things that you could see. I believe they started with that image letting you know that the aliens turn was starting, and then it would flash in between the still image with alien sounds and people dying, then the things you could see it would show, like this game does, and then there was text saying it was the start of XCOM's turn either in the center of the screen on or the still image, but it was clear. I felt that this added suspense and made me feel like I was a part of the mayhem, I couldn't see it but I could hear it and knew that it was out there. Something like that was much better than green light/ red light.
