Large language model (LLM)–powered services are gaining popularity in various applications due to their exceptional performance in many tasks, such as sentiment analysis and answering questions. Recently, research has been exploring their potential use in digital health contexts, particularly in the mental health domain. However, implementing LLM-enhanced conversational artificial intelligence (CAI) presents significant ethical, technical, and clinical challenges. In this viewpoint paper, we discuss 2 challenges that affect the use of LLM-enhanced CAI for individuals with mental health issues, focusing on the use case of patients with depression: the tendency to humanize LLM-enhanced CAI and their lack of contextualized robustness. Our approach is interdisciplinary, relying on considerations from philosophy, psychology, and computer science. We argue that the humanization of LLM-enhanced CAI hinges on the reflection of what it means to simulate “human-like” features with LLMs and what role these systems should play in interactions with humans. Further, ensuring the contextualization of the robustness of LLMs requires considering the specificities of language production in individuals with depression, as well as its evolution over time. Finally, we provide a series of recommendations to foster the responsible design and deployment of LLM-enhanced CAI for the therapeutic support of individuals with depression.