Recent progress in large language models has led to applications that can (at least) simulate possession of full moral agency due to their capacity to report context-sensitive moral assessments in open-domain conversations. However, automating moral decision-making faces several methodological as well as ethical challenges. They arise in the fields of bias mitigation, missing ground truth for moral “correctness”, effects of bounded ethicality in machines, changes in moral norms over time, risks of using morally informed AI systems as actual advice, as well as societal implications an increasing importance of algorithmic moral decision-making would have. This paper comments on all these challenges and provides critical considerations for future research on full artificial moral agency. Importantly, some of the adduced challenges can be met by more careful technology design, but others necessarily require engagement with core problems of meta-ethics.