Seeing with one eye, why intensity doesn't get half?
Think of eyes as cameras producing an image at a given framerate. If you have 2 cameras and shut 1 of them off, that doesn't change the amount of light incoming to the other camera.

Your question is one of signal interpretation rather than receiving signals and adding them. Given that the 2 cameras have different perspectives, adding their respective pixels makes no sense. Instead, the dual images (if both cameras are on) are post-processed for spatial reference relevant to perspective.

In the case where a camera is shut off, then the spatial reference becomes a null picture and the post-processing can be skipped.

(For reference, if you took incoming data from both eyes and added them, the result would be an incoherent and largely unusable mess)