Is WAEC/NECO compulsory?

My simple answer is that you should do whatever it takes to ensure that you have a great college to attend whether it is in the US, UK, or Nigeria. If you opt out of those exams and put all your eggs in the Stanford basket, that is a risky move because it is extremely difficult for International students to get admitted into top American colleges even with perfect test scores and grades.

US Colleges do not look at local country exam results as part of their admissions process. It would be complete mess if they did. However, it's your duty as an applicant to effectively communicate that you are a great student with great grades, course rigor, ECs, other talents and evidence of intellectual vitality.

I recall, I might be incorrect in my thinking but I understand Nigeria has compulsory education from 6-15 years of age. So whence you graduate, you will be significantly younger than most applicants who apply to Stanford. This may not work to your advantage because most successful admits have at least K-12 (13 years of formal education prior to applying. This means they have taken more APs, IBs, and Honors courses that perhaps you were exposed to and have had other opportunities to develop their ECs, passion projects and venture on academic adventures like internships, independent study and similar things.

If you are serious about applying to Stanford at age 15-16, I would make sure you had a back up plan as well. I don't know your family situation or financial situation, but I highly recommend looking into a UK or US or Swiss Boarding school where you can fortify your academic narrative and ECs for 1 or 2 years. That would certainly improve your odds at Stanford or other Elite universities. If you are very smart, most of the best boarding schools offer admission Need Blind and have sufficient coffers to cover full ride scholarships.

Good luck.