> then I was really annoyed (never dealt with vertex maps so far)
> that I couldn't get the clue, even when switching off the smooth
> option in the assigned material, why there wouldn't be any
> facets at all.

Because a vertex map is active, any change of the smoothing angle in the surface editor isn't take into account.
To remove the vertex map :

List / Other maps / Right click on Vertex map and choose delete.