Using continuum elasticity theory and an eight-band k·p formalism, we study the electronic properties of GaN nanowires with axial InxGa1-xN insertions. The three-dimensional strain distribution in these insertions and the resulting distribution of the polarization fields are fully taken into account. In addition, we consider the presence of a surface potential originating from Fermi level pinning at the sidewall surfaces of the nanowires. Our simulations reveal an in-plane spatial separation of electrons and holes in the case of weak piezoelectric potentials, which correspond to an In content and layer thickness required for emission in the blue and violet spectral range. These results explain the quenching of the photoluminescence intensity experimentally observed for short emission wavelengths. We devise and discuss strategies to overcome this problem.