Can grout be used as cement? Why or why not?

Technically, yes. Practically, there are far better choices.

Let’s assume you are talking about tile grout.

Its job is to bond to ceramics or stone and provide a strong wear surface. We really use a wide array of different materials that we call grout for this job, but as long as they do the two jobs, great.

Cement, specifically concrete cement, is a bulk binder with great strength characteristics (except for tensile strength, yes I know). Comparatively, concrete cement is also very inexpensive than most tile grouts.

So, while you can find specific grouts that would work well as a concrete cement, there are just too many better choices.