There are two reasons:
(1) Lagrange method is a new knowledge point, so you should get used to learning and applying new knowledge.
(2) Using Lagrange method, it is convenient for teachers to mark papers, and it is convenient for teachers to facilitate themselves. There are so many postgraduate papers and so many marking teachers. Not every teacher is willing to take the time to "understand" you and your alternative problem-solving process.
If your answer is wrong, your problem-solving process is different, and the teacher may not be very interested. Your risk of being deducted points has increased.
If your answer is wrong, your problem-solving process conforms to the reference answer, and you will get many points. (Your risk of losing points is reduced)
For reference only!