Ferroelectric field-effect doping has emerged as a powerful approach to manipulate the ground state of correlated oxides, opening the door to a new class of field-effect devices. However, this potential is not fully exploited so far, since the size of the field-effect doping is generally much smaller than expected. Here we study the limiting factors through magneto-transport, scanning transmission electron and piezo-response force microscopy in ferroelectric/superconductor (YBa2Cu3O7-{delta} /BiFeO3) heterostructures, a model system showing very strong field-effects. Still, we find that they are limited in the first place by an incomplete ferroelectric switching. This can be explained by the existence of a preferential polarization direction set by the atomic terminations at the interface. More importantly, we also find that the field-effect carrier doping is accompanied by a strong modulation of the carrier mobility. Besides making quantification of field-effects via Hall measurements not straightforward, this finding suggests that ferroelectric poling produces structural changes (e.g. charged defects or structural distortions) in the correlated oxide channel. Those findings have important consequences for the understanding of ferroelectric field-effects and for the strategies to further enhance them.