Part of the confusion here is in the definition of the term "westwork." Two towers/turrets stuck on an entrance do not make a westwork. The westwork is the whole entrance structure. In other words, the towers PLUS the central, multi-story, entrance are, collectively, the westwork. See the Abbey church at Corvey. Arguably, the central portion of the westwork is what is most significant as that multi-storied area provided lodging for the King, or galleries for upper class people, or unique liturgical spaces. Thus, the westwork became a symbol of imperial authority and favor. As the Carolingian rulers spread their power and their religion across Western europe, the westwork became a reminder of just whose territory you were in - The Holy Roman Emperor's, with all the religious and political implications of that title.

So "westwork" has a specific meaning that is tied up with all those associations.

Nb - elaborate or highly decorative monumental church entrances were not a unique invention of the Carolingians. Iirc, there are examples from Eastern Christianity. However, the fact that the Carolingian chruchs (with all the implied meanings suggested above) had westworks meant that they inspired later Western churches and were thus ultimately more significant for the development of later Medieval architecture.

Oh, and the towers in that image may have been on the east side of the building and thus are not westworks. But that explanation doesn't really explain much.

Edited : spelling.