Why is it used?
Chiefly, because it is easily automated. This kind of topology is most often the result of automation; Booleans. where the intersection between surfaces is programatically calculated, or automatic conversion from other data-formats.
What is the benefit and utility?
Apart from the above, none in particular.
There can be disadvantages.
- If modelling by hand, the topology does not play well with polygonal modelling systems, including Blender, that are geared to the selection and manipulation of loops and rings of edges bounding 'tracks' of quadrilateral faces.
- The reason quads are emphasized is that, if quad face-loops flow across polygonal surfaces in a way that echoes an underlying approximated curvature, then when they are triangulated by a renderer, and the normals are interpolated by a smooth-shading algorithm, the normals approximate those of the smooth curved surface more accurately. Especially under Catmull-Clark subdivision, which is a common modelling target.
- Correctly flowing quad face-loops deform well, where that is called for, by animation or subsequent modelling techniques. There are no unexpected creases or kinks in deformed surfaces.
Wherever surfaces do not have to be accurately smooth-shaded, either in their modelled form, or under subsequent deformation, (because they are geometrically flat, or shaded flat,) there is no great harm in non-quad topology, but for ease of modelling, you may choose to avoid it. If a curvature is more accurately approximated by sheer density of polygons, the computational cost may be high, but the question becomes less relevant.