the thing that convinced me to switch to elaborately showing my work was partial credit. in the competitive tests, if you didn't know the correct answer, you'd look at the next 3 questions to see if you could answer them. a skipped answer was counted as wrong, and points deducted. since the test increased in difficulty as you progressed, you'd have to consider how many questions you were skipping and if it was better to just stop.
in classes, even if the answer was incorrect, if you showed your work you could receive partial credit. if it was clear you were using the right steps to get there but forgot to carry a one or skipped a step somewhere else but it was clear that the basic understanding on how to solve the problem was close, you could avoid a big goose egg for that question. IIRC, the AP exams were like that as well. more about showing understanding of the process than just the correct answer is what they were trying to achieve.
in classes, even if the answer was incorrect, if you showed your work you could receive partial credit. if it was clear you were using the right steps to get there but forgot to carry a one or skipped a step somewhere else but it was clear that the basic understanding on how to solve the problem was close, you could avoid a big goose egg for that question. IIRC, the AP exams were like that as well. more about showing understanding of the process than just the correct answer is what they were trying to achieve.