The difficulty of anonymizing text data hinders the development and deployment of NLP in high-stakes domains that involve private data, such as healthcare and social services. Poorly anonymized sensitive data cannot be easily shared with annotators or external researchers, nor can it be used to train public models. In this work, we explore the feasibility of using synthetic data generated from differentially private language models in place of real data to facilitate the development of NLP in these domains without compromising privacy. In contrast to prior work, we generate synthetic data for real high-stakes domains, and we propose and conduct use-inspired evaluations to assess data quality. Our results show that prior simplistic evaluations have failed to highlight utility, privacy, and fairness issues in the synthetic data. Overall, our work underscores the need for further improvements to synthetic data generation for it to be a viable way to enable privacy-preserving data sharing.