Quads are great because they provide a defined flow: for each edge there’s exactly one opposite edge. Technically that’s true for all even-sided polygons, but quads offer minimal ambiguity after triangles (you can only split a quad two ways, whereas there are multiple ways of splitting n-gons).

Numerous algorithms take advantage of that. Loops, rings, subdivision… It’s easy to define and control curvature with quads. So they are the best practical primitive for authoring.

Just imagine editing that mesh if all you had was triangles - no loop and ring selection, most always twice the polygons to select each time, no Loop Cut tool, no useful edge sliding, etc… Or, triangulate it and see what the Subdivision Surface would do with the shapes