The best argument I know of for showing work is that it will help you get partial credit if you make a dumb arithmetic error.
Exactly this. When you show your work, you get points no matter what the answer is - lesser points if the steps are correct and full points if the answer is correct too.
In my child's school, they are "taught" how to show their work for both word problems and numerical calculations. They expect a certain format and show the kids how to do it and they get point deductions if that is not followed.
My DS is adpet at mental math (regrouping mentally and doing anzan calculations in his mind), but he still does the manual steps on the paper as the teacher wants him to. I tell him to recheck his work using his mental math strategies while still showing his work on paper.
If your friend is in a homeschooling scenario, I don't think that showing the steps is necessary in the early elementary stages because who really wants to draw bar graphs or pictures for all addition, subtraction, multiplication problems? In such a case, I think that showing steps only for word problems is good enough. But, that is just my opinion...
ETA: just noticed that you said "traditional school" - sorry, the giftie needs to learn that the teacher is the person giving out the grades and they need to do things the teacher's way in the classroom
