This would be a good question for JoAnna. I would think the lubrication properties of bar soap would be almost nonexistent. Plus I would think it would aid in making the face to dry..
I've tried bar soap to shave. The lather just isn't as thick. It works, just isn't as luxurious as shave soap.
I occasionally shaved with bar soaps instead of canned shaving creams in an emergency, before I even discovered there was such a thing as a a shaving soap. Building up a thick lather without a brush and with only Ivory soap is challenging, but beats dry shaving. I've got a uniquely scented bath soap called Grandpa's Pine Tar Soap, which they have for less than that Amazon price at my local supermarket. I've heard that it will work as a shaving soap, but have never gotten around to trying it.
Most bath soaps make lousy shave soaps (yes, I tried a few). Dove is one of the notable exceptions. La Compagnie de Provence brand Savon de Marseille is another, and works quite well as a shaving soap. I assume that other Savon de Marseille brands also make good shaving soaps.
I shaved with Dove many times in the past if I had no cream or soap when I was travelling, and I was able to get a pretty good and acceptable lather with my brush. The skincare was also good.