As Artificial Intelligence (AI) becomes more pervasive in our society, it is crucial to develop, deploy, and assess Responsible and Trustworthy AI (RTAI) models, i.e., those that consider not only accuracy but also other aspects, such as explainability, fairness, and energy efficiency. Workflow provenance data have historically enabled critical capabilities towards RTAI. Provenance data derivation paths contribute to responsible workflows through transparency in tracking artifacts and resource consumption. Provenance data are well-known for their trustworthiness helping explainability, reproducibility, and accountability. However, there are complex challenges to achieve RTAI, which are further complicated by the heterogeneous infrastructure in the computing continuum (Edge-Cloud-HPC) used to develop and deploy models. As a result, a significant research and development gap remains between workflow provenance data management and RTAI. In this paper, we present a vision of the pivotal role of workflow provenance in supporting RTAI and discuss related challenges. We present a schematic view between RTAI and provenance, and highlight open research directions.