If you remove A as a choice, or B, people might go with their next preferred option instead of just not voting at all, etc.

This means you can't know for sure that results would equal the same with or without that option, because you cannot actually assume all actors will vote the same every time. To even begin to think such a thing as true is just asinine when the world proves to us on a daily basis that people are willing to compromise on their beliefs all the time. (No offense.)