The parent to this comment said

> It works fine for songs that modulate.

By definition, modulation is the act of not remaining diatonic. Modulation = changing keys. Diatonic = staying within key.

So, no, we don't need to assume anything about diatonicity in order to successfully do harmonic analysis using Roman numerals.

I always thought of diatonic as playing within a harmonized major/minor scale, even if you change keys. What I'm talking about is music that doesn't obey the rules at all, doesn't have a key, doesn't change keys, it's just random chords thrown together because the artist thought they sounded good. Changing to another key is still playing in a key. Many rock musicians wouldn't know a key if it bit them in the ass.

Why do you need that assumption? I think Roman numerals allow for non-diatonic chords like a i diminished.

Roman numerals still presume you're playing on a harmonized scale in a key; not all music fits that as many rock musicians don't know what a key is and pick chords randomly by sound, not by knowing anything about music theory.