> When two triangles form a quad, the entire area along the diagonal "seam" will be rendered twice
This may be true, but I'm pretty sure that this is more than made up for by the additional pixels in the single triangle circumscribing the quad. In fact, I'm willing to bet that it's a mathematical certainty for any rectangle, although I didn't do enough of the math to prove it.
Instead, I would say that most rendering, especially of hundreds of thousands of 2D shapes, are going to be pixel limited. So trading pixels for vertices is a poor trade.