The upgrade of IceTop, the surface array of IceCube, by a hybrid array of scintillation and radio detectors is motivated by a rich science case. The scintillators will lower the threshold for the measurement of air showers to about 100 TeV, provide a more efficient veto of air showers for neutrino measurements, and improve the separation of the electromagnetic and muonic shower components due to the different responses of scintillators and ice-Cherenkov tanks. Furthermore, the scintillators will enable the calibration and compensation of the effect of snow accumulation above IceTop. The radio antennas will provide a calorimetric measurement of the electromagnetic shower component and a direct sensitivity to the shower maximum. Consequently, the combination of the existing ice-Cherenkov detectors in the ice and at the surface with the new scintillation and radio detectors at the surface will enable unprecedented accuracy for event-by-event mass classification in the PeV to EeV range. This will transform IceCube into the most accurate instrument for high-energy Galactic cosmic rays in the Southern Hemisphere. Hence, the hybrid array will make an important contribution to the main science case of IceCube of understanding the origin of cosmic rays. In addition to its cosmic-ray science goals, the hybrid array provides essential RD for IceCube-Gen2 which will feature a larger surface array, sophisticated timing and communication technology, and elevated surface structures. Moreover, the hybrid array will improve the understanding of the atmospheric background to the neutrino measurements suffering from uncertainties in the absolute flux and the mass composition, and from deficiencies of hadronic interaction models. Finally, the hybrid array opens new scientific opportunities, such as the searches for PeV gamma rays from the Galactic Center and for mass-dependent anisotropies, which both may lead to the discovery of the most energetic sources in the Milky Way.