To fully exploit the potential of computational phylogenetic methods for cognate data one needs to leverage specific (complex) models an machine learning-based techniques. However, both approaches require datasets that are substantially larger than the manually collected cognate data currently available. To the best of our knowledge, there exists no feasible approach to automatically generate larger cognate datasets. We substantiate this claim by automatically extracting datasets from BabelNet, a large multilingual encyclopedic dictionary. We demonstrate that phylogenetic inferences on the respective character matrices yield trees that are largely inconsistent with the established gold standard ground truth trees. We also discuss why we consider it as being unlikely to be able to extract more suitable character matrices from other multilingual resources. Phylogenetic data analysis approaches that require larger datasets can therefore not be applied to cognate data. Thus, it remains an open question how, and if these computational approaches can be applied in historical linguistics.