One of the key cost drivers in television filming today is the single-camera technique, in which each scene is filmed several times with a single camera in different camera angles, in order to get the lighting optimal.
You can use a flying-spot camera to do much of this in a single shot using multiple photosensors, each one corresponding to a different virtual light source, all filmed from the point of view of the flying-spot illumination source. This allows you to make a weighted sum of the signals from the various light sensors after the fact in order to compute a version of the scene with the proper “lighting”.
This doesn’t allow you to change camera angles (without multiple flying-spot sources and the attendant difficulties with higher-speed signals), but in many cases all that is needed is to crop a higher-resolution shot down to the area of interest.
The standard approach since the 1950s to making flying-spot stages livable for the actors is to illuminate them during the vertical blanking interval with a strobe light.