PTEX sounds interesting and I'll support anything that removes the necessity of UV mapping, but the insistance of quads in the higher end 3D spectrum has been the norm much longer than ptex has existed, so that can't be the reason. 

Consistently even edgeflow is a given, whether you're using all quads, all tris or a combination of the two.

Quads won't produce artifacting  - if the geometry is designed correctly to begin with. I guess I should have added that part in before. The only other time they'll produce artifacting is if poly faces are intersecting each other. If you're having to try and twist quads around to distort them into the needed edgeflow then that means the mesh wasn't designed properly to allow for the mesh to change direction. 

Quads isn't the only rule tho. Along with it you have to consider consistently even edgelfow, as pointed out (should be obvious but I guess not), no stars containing more than 5 points, no n-gons, using diamonds to direct flow. Diamonds can be tricky, as their base shape reduces to a tri, so a good understanding of where and when to use them is important. Starting with the most basic shapes when you begin a new model, just like with drawing, is also important. A lot of people just learning to model insist on dividing the model up until it's smooth before they start working on it, (this is especially common in sculpting programs), when instead you should be pulling 4-6 sided cubes around until you get the basic shape needed, and then add edges gradually, and only to round out forms, once the edges you have are stetched to their absolute max. 

 

~Shane