Perhaps more succinctly, you always write any two consecutive notes of a diatonic scale on two different lines of the staff. It would be bad if your in-key scale looked like it had two notes on the same line and then a jump of a third. Note this is true even when you have accidentals! It’s a way to keep the intention or semantics of notes more clear, and more easily readable, regardless of the pitch interval. Like how the article talks about the distinction between an augmented 2nd and a diminished 3d, the notation is designed to help clarify that distinction.