I can relate to the frustration. If we based the success of a group solely on the diversity of the lineage, then the genus Homo would be a resounding failure. Our heyday was 10K–1M years ago when there was 16 + species spread around the globe. Geologically we appear to be on our way out (and I suspect that as geological time progresses this will prove to be true), but in the current day and age we are a mighty successful species. One might even argue we are too successful.
Another notable problem with paleo-diversity measures is the arbitrary designation of species. Few species meters are the same, and paleo species are even worse. Who is to say that the skeleton we associate with Triceratops horridus, wasn't the archetype for a dozen or more species of Triceratops (with potentially a few genera interspersed in there). Those of us on this list are well aware of the near identical skeletons between lions and tigers. That degree of similarity is likely multiplied ten fold for extinct species, few of which are known from complete skeletons. It's a fair bet that we are grossly underestimating species richness for extinct organisms, even when considering the generally lower species richness of larger animals (though, again, your species meter may vary).
I applaud what Sakamoto et al., and others before them are trying to do, but I don't think that the small-scale evolutionary patterns that ecologists study are possible in the time-averaged rocks that paleontologists look at.
All that said, I would think that an apples to apples approach (looking at related, extinct groups only) might give a good first approximation for lineage health, which is likely the best we'll get. Even then, though, this seems to work better for the invert paleo workers, since they have the necessary sample sizes.