For the first time, the predictive capabilities of the mixed Bohm/GyroBohm, Weiland and 'retuned' GLF23 transport models are investigated with ITB discharges from the ITPA ITB database with fully predictive, time-dependent transport simulations. A range of plasma conditions is examined for JET, JT-60U and DIII-D discharges with ITBs. The simulations show that the Bohm/GyroBohm model is able to follow the time evolution of the discharge from the preheating phase without an ITB through the ITB onset phase until the high performance phase within a fair accuracy in most cases in JET and JT-60U. This indicates the importance of the interplay between the magnetic shear and ωE×B flow shear in ITB formation since these are the mechanisms that govern the ITB physics in the model. In order to achieve a good agreement in DIII-D, the α-stabilisation had to be included into the model, emphasising the role played by the α-stabilisation in the physics of the ITBs. The Weiland and GLF23 transport models show limited agreement between the model predictions and experimental time evolution of the ITB and kinetic plasma profiles. TheWeiland model does not to form a clear ITB in any of the three tokamaks despite varying plasma profiles, such as the q-profile. On the other hand, the average temperatures and density are often in fair agreement with experimental values. The GLF23 model often predicts an ITB, but its radial location is often too far inside the plasma, or shrinks as the simulations proceed in time. Consequently, the central temperatures at the end of the simulations during the high performance phase are usually underestimated. Worth noting is that GLF23 features in general better predictions of the Te and Ti profiles outside the ITB than the other models studied. Achieving the quantitative capability to predict the multichannel ITB dynamics with fully predictive, time-dependent transport simulations has turned out to be extremely challenging.