Radar perception models are trained with different inputs, from range-Doppler spectra to sparse point clouds. Dense spectra are assumed to outperform sparse point clouds, yet they can vary considerably across sensors and configurations, which hinders transfer. In this paper, we provide alternatives for incorporating spectral information into radar point clouds and show that, point clouds need not underperform compared to spectra. We introduce the spectral point cloud paradigm, where point clouds are treated as sparse, compressed representations of the radar spectra, and argue that, when enriched with spectral information, they serve as strong candidates for a unified input representation that is more robust against sensor-specific differences. We develop an experimental framework that compares spectral point cloud (PC) models at varying densities against a dense range-Doppler (RD) benchmark, and report the density levels where the PC configurations meet the performance of the RD benchmark. Furthermore, we experiment with two basic spectral enrichment approaches, that inject additional target-relevant information into the point clouds. Contrary to the common belief that the dense RD approach is superior, we show that point clouds can do just as well, and can surpass the RD benchmark when enrichment is applied. Spectral point clouds can therefore serve as strong candidates for unified radar perception, paving the way for future radar foundation models.