Following the proposal by Tsafnat et al (2024) to converge on three open health data standards, this viewpoint offers a critical reflection on their proposed alignment of openEHR, Fast Health Interoperability Resources (FHIR), and Observational Medical Outcomes Partnership (OMOP) as default data standards for clinical care and administration, data exchange, and longitudinal analysis, respectively. We argue that open standards are a necessary but not sufficient condition to achieve health data interoperability. The ecosystem of open-source software needs to be considered when choosing an appropriate standard for a given context. We discuss two specific contexts, namely standardization of (1) health data for federated learning, and (2) health data sharing in low- and middle-income countries. Specific design principles, practical considerations, and implementation choices for these two contexts are described, based on ongoing work in both areas. In the case of federated learning, we observe convergence toward OMOP and FHIR, where the two standards can effectively be used side-by-side given the availability of mediators between the two. In the case of health information exchanges in low and middle-income countries, we see a strong convergence toward FHIR as the primary standard. We propose practical guidelines for context-specific adaptation of open health data standards.