The problem is that the underlying format you are saving as does not understand anything other than a 24bit per pixel colour. If the underlying container or format specifically catered for 8-bit grey scale (or 8-bit formats in general) then you would see the size reduction you ate expecting.
As an example you can save an image as a .BMP or PNG you usually get the option to set the bit depth for the output (you do if you are using Paint.NET at least) then converting to grey scale will see a benefit.
JPEG does not strictly support lower bit depths if I remember correctly, I would be surprised if most modern video encoders did either as 99% of their use is for colour sources.