In the past two decades, research in visual analytics (VA) applications has made tremendous progress, not just in terms of scientific contributions, but also in real-world impact across wide-ranging domains including bioinformatics, urban analytics, and explainable AI. Despite these success stories, questions on the rigor and value of VA application research have emerged as a grand challenge. This article outlines a research and development agenda for making VA application research more rigorous and impactful. We first analyze the characteristics of VA application research and explain how they cause the rigor and value problem. Next, we propose a research ecosystem for improving scientific value, and rigor and outline an agenda with 12 open challenges spanning four areas, including foundation, methodology, application, and community. We encourage discussions, debates, and innovative efforts toward more rigorous and impactful VA research.