Artificial intelligence (AI) could transform the public sector by boosting efficiency, cutting costs, and improving services. Yet current efforts remain fragmented, small-scale, and risk-focused. This paper identifies three blind spots that limit progress and uses Theory U to frame solutions, considering the AI Act, KIVO draft, trustworthy AI, and ethics. First, AI is judged mainly by its outputs or processes, while the “place of origin”—the conditions shaping adoption—is overlooked. Second, AI is often treated only as a risk, without comparing it to human-based alternatives that also contain biases and inefficiencies. Third, AI is excluded as an active part of decision-making, despite its potential to add value through data, connectivity, and probabilistic reasoning. The central claim is that AI must be integrated into the very point where decisions about its use are made. Recognizing AI as both relational and intrinsic to governance design is essential to move beyond current dysfunctions. Doing so will unlock its transformative potential, ensure compliance and ethics, and support the development of trustworthy AI in the public sector.