A superintense laser pulse illuminating a thin solid-density foil can, in principle, accelerate the entire foil, therefore yielding dense, collimated, and quasi-monoenergetic ion beams. These unique features render radiation pressure acceleration in the light sail regime a promising acceleration mechanism suited for applications where dense and high-flux ion beams are required. However, the onset of several instabilities typically results into foil deformation and heating, which cause premature termination of the radiation pressure acceleration stage and strong broadening of the ion spectrum. Here we show that (i) a relation between the attainable ion energy per nucleon and the development of instabilities exists, such that increasing the ion energy results into an increase of transverse modulation effects and, (ii) that the above relation can be weakened with proper matching of laser pulse-foil parameters, such that high-energy dense ion beams with high-quality spectral features can be produced.