Should phylogenetic models be trying to "fit an elephant"?

For the past two decades, there has been an ongoing debate within the plylogenetics community over whether model-based approaches for molecular systematics (such as maximum likelihood) should be preferred over the more traditional "maximum parsimony" approach. A recent simulation study by Kolaczkowski and Thornton has brought this debate into sharp focus. In this article, I discuss the significance of their findings and offer a prognosis on the implications for molecular phylogenetics. I believe that biochemistry and model selection have an important role in developing accurate phylogenetic approaches.