It could've come out of the flat topped helmets wanting to move thw point of impact away from the head as well as the face, similar to burgonets having combs and brims.
A flat top sits taller than conical helmets, much like a bascinet sits a fair height above the skull, however, they also sit a bit out, offering protection from downward blows by moving the point of impact further out from the head.
If this then gradually shrunk to accomodate for a more slanted glancing surface underneath, it follows that they didn't redesign the top until it got small enough to where they turned into sugarloafes and Pembridge tops.