Someone else can probably provide a better explanation, but my understanding is that all of the inputs are bridged for simplicity; specifically composite video, luma on S-Video, and luma on component are bridged, as well as chroma on S-Video and red on component (I believe it’s red), because these lines share a common input on the video processor. The “input” toggle simply changes how the processor treats the connected lines.
So, if you were to have all three hooked up, when you turn one on, current from that video line could leak down the other video cables, which can both leak current into those consoles as well as weaken or potentially interrupt the signals received by the video processor, neither of which is desirable.