Hand fatigue is usually a pretty minor thing. Being ambidextrous won't prevent it either. Often, just shifting your grip regularly is enough to prevent it.
Most things which would prevent you from using one hand will affect both, like arthritis. Practicing such a difficult skill to have a backup seems excessive.
An ambidextrous artist can use whichever hand will produce a desired mark best. No matter what, there will be differences between the marks produced by each hand. Even if they were perfectly physically symmetrical, (which they never are) the very fact that they are mirrors of each other means certain directional marks will be easier to make with one hand or another. Our hands move in natural ways easiest. Having an opposite hand which can do the "unnatural" direction for the other would be a good thing. Also, because the two hands will have subtle structural differences, it is likely they would have their own unique marks.
An ambidextrous artist can reach into their composition from any direction. Many mistakes come down to the artist's palm, wrist, or arm interfering with the work. Often, we cover our composition, partially blinding ourselves while we work. Sometimes, we smudge our work while we draw somewhere else on the page. An ambidextrous artist could always take the path which minimizes the negative effects of having arms.
An ambidextrous artist could, if the page is fixed in place, use both hands to create combined marks that nobody else can make.