What is the technical reason why Quads are preferred over triangles in subsurface modeling? Every layer beyond the original model will be quaded regardless of what the polygons were like before you started, at least while using Catmull-clark method this is true.
Try to subdivide a triangulated model and the same with quads.You should notice that subsurfing quads produces much better distribution of polys. It’s because of the algorythm.
There are some algorithms available that work on triangles only. And they do that extremely well. Much better than Catmull-Clark.
The advantages of quads are obvious though. It is much easier to modify loop/pole based quad mesh than a mesh consisting purely of triangles.
There might be some special cases in which algorithm purely for triangles would be useful though.
If you want to find more information about these algorithms, dig through old Siggraph course notes.