Does streaming videos in gray scale consume less bandwidth, than a regular color video. I want to believe it does because the data about color would not have to be sent. But I might be wrong.
It might surprise you, but as far as mainstream streaming technologies are concerned, not only there is no such thing as a grayscale video, there is no such thing as RGB video either. Those videos are encoding in YUV color format. (Well, that, and Y'UV, YCbCr, Y'CbCr, YPbPr, Y'PbPr)
But does the strictly-gray gamut compress better than the full spectrum? It is impossible to say off-hand. Compression schemes are too complex.