The exploding power consumption of AI and cloud datacenters (DCs) intensifies the long-standing concerns about their carbon footprint, especially because DCs' need for constant power clashes with volatile renewable generation needed for grid decarbonization. DC flexibility (a.k.a. load adaptation) is a key to reducing DC carbon emissions by improving grid renewable absorption. DC flexibility can be created, without disturbing datacenter capacity by decoupling a datacenter's power capacity and grid load with a collection of energy resources. Because decoupling can be costly, we study how to best distribute and manage decoupling to maximize benefits for all. Key considerations include site variation and datacenter-grid cooperation. We first define and compute the power and energy needs of datacenter load decoupling, and then we evaluate designed distribution and management approaches. Evaluation shows that optimized distribution can deliver >98% of the potential grid carbon reduction with 70% of the total decoupling need. For management, DC-grid cooperation (2-way sharing and control vs. 1-way info sharing) enables 1.4x grid carbon reduction. Finally, we show that decoupling may be economically viable, as on average datacenters can get power cost and carbon emissions benefits greater than their local costs of decoupling. However, skew across sites suggests grid intervention may be required.