The European Union's climate policy architecture is fragmented, with multiple compliance mechanisms and varying carbon prices and rules shaping resource allocation for emissions reduction. This fragmentation leads to economic inefficiencies and higher costs, as resources are shuffled between mechanisms, creating a complex and costly transition. The challenge is to move from this patchwork of policies to a unified framework with a uniform carbon price. The interconnectedness of the EU economy and energy system will drive price convergence through arbitrage opportunities, but direct and indirect arbitrage can lead to misallocation and inefficiency. To address this, a controlled-convergence approach is proposed, linking different compliance mechanisms to the EU Emissions Trading System (ETS) as a hub. This would streamline the architecture, offering integrity and creating a market by design. Gradual linkage, focusing on marginal mitigation units and managing the interface, is essential to tackle distributional challenges and ensure ambition is not watered down. A staged pathway, emphasizing learning and governance overhaul, is crucial for political feasibility and efficiency. This approach avoids rent-seeking and costly regulations, reducing the burden on society and signaling to market participants that inefficient arbitrage is not worthwhile.