I add both oil and salt in the very beginning, because there’s no reason to not do that.
If you really like to impregnate your pasta, so that it won’t absorb your sauce (or less well), then you are right about the there-is-no-reason-part in your answer.
It depends on the pasta (form, freshness, self-made… etc). Some has to be stirred 3-4 times others just once, in my experience.