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In present-day fusion devices, central wave heating is crucial to avoid core tungsten (W) accumulation. In this work, we present an integrated modelling framework that reproduces the reduction of core W peaking in ASDEX Upgrade experiments when multiple transport channels are self-consistently evolved, emphasizing the effects of wave heating on turbulent and neoclassical W transport. Predictions for the ITER 15 MA baseline are then provided. We show that the core of a reactor is in a different transport regime for W as compared to present-day tokamaks. The challenges introduced by W arise from global radiation losses that can hinder operation in H-mode, instead of local central accumulation.