The water-energy-food nexus (WEFN) offers an integrative lens for managing interdependent resources, but current models often overlook the systemic constraint that not all subsystem goals can be simultaneously fulfilled due to limited coordination capacity. In this study, we proposed the Impossible Supply Triangle Hypothesis, which formalizes this constraint and introduces the Goal Fulfillment Ratio (GFR) as a normalized metric of subsystem goal attainment. Based on this framework, we conducted a spatiotemporal assessment of WEFN supply, demand, and coordination dynamics in China's Mu Us Sandy Land from 2000 to 2020. The GFR analysis revealed that 10.33 % of the region entered a resource conflict state in 2020 with conflict zones primarily concentrated in the counties of Dingbian, Yijinhuoluo, Yanchi, and Jingbian. Sensitivity analysis confirms the triangle model's validity: as the coordination threshold decreases from 2.2 to 1.8, the conflict ratio rises sharply from 2.98 % to 93.07 %, indicating heightened systemic stress near the threshold. Supply-Demand Match Degree (SDMD) analysis showed average matching degrees in 2020 of 0.0115 (water), 0.0034 (energy), and -0.0038 (food), indicating relative surpluses for water and energy, and deficits for food. Root Mean Square Deviation trade-off assessment identified Jingbian, Hengshan, and Yijinhuoluo as the counties with the highest supply-side imbalances. Scenario simulations showed that a 10 % economic recession increased water SDMD by 13.57 %, while a 10 % population decrease raised energy SDMD by 23.16 %. These findings demonstrate that the Goal Fulfillment Ratio-Supply-Demand Match Degree-Root Mean Square Deviation framework can effectively reveal structural risks and coordination limits in WEFN systems, providing a replicable tool for integrated resource governance.