Operation with beam heating is prone to central accumulation of high-Z impurities in present-day tokamaks due to a dominant neoclassical pinch. Fusion reactors are expected to have a different core transport regime for high-Z impurities, where turbulent transport completely dominates in both diffusion and convection, causing flat impurity profiles. In this work, we present integrated simulations of plasmas that approach this regime of less dominant neoclassical and stronger turbulent high-Z impurity transport in three tokamaks: ASDEX Upgrade, JET and Alcator C-Mod. The modelling is first validated against a suite of diagnostics measuring both the main plasma and the impurity profiles. The high-Z impurity densities are found to be flat in both experiments and simulations. The impurity transport coefficients as calculated by theory-based turbulent and neoclassical transport models are then analysed, showing comparable or even dominant turbulent components instead of the more typical dominant neoclassical high-Z impurity convection. The implications for a reactor are discussed.