Ethics is one of the longest standing intellectual endeavors of humanity. In recent years, the fields of AI and NLP have attempted to address issues of harmful outcomes in machine learning systems that are made to interface with humans. One recent approach in this vein is the construction of NLP morality models that can take in arbitrary text and output a moral judgment about the situation described. In this work, we offer a critique of such NLP methods for automating ethical decision-making. Through an audit of recent work on computational approaches for predicting morality, we examine the broader issues that arise from such efforts. We conclude with a discussion of how machine ethics could usefully proceed in NLP, by focusing on current and near-future uses of technology, in a way that centers around transparency, democratic values, and allows for straightforward accountability.