Hi,
first of all I am confused by a few of your statements.
Using a focal reducer does increase your field of view, and the photons are spread over fewer pixels, but you will be getting more arc seconds of sky per pixel, so your pixel scale will go up.
so yes as you will be getting more light then you can lower the exposure.
as for binning, if,you bin 2x2 in the camera, and you have say 5 micron size square pixels, then after binning those pixels are now 10 micron size in effect and twice as sensitive as before so it makes the camera a lot more sensitive, but at the cost of halving the resolution, but you are still imaging the same amount of sky, so the image will be the same but lower resolution when binning.
binning in the software will not give you the same effect, as hardware binning in the camera.
so the reducer and binning are two completely different things, and binning in the software will not increase your FOV like the reducer will, so there is no way binning can take the place of a focal reducer, as it would have to alter the FOV of the image to do that, and it doesn't, it just lowers the resolution, but makes the camera more sensitive.
so the two things are completely different.
i hope that all makes sense, and is of some help.
AB