In this paper, we investigate the benefits of teaming up data from the radio to the far-infrared (FIR) regime for the characterization of dusty star-forming galaxies (DSFGs). These galaxies are thought to be the star-forming progenitors of local massive quiescent galaxies and to play a pivotal role in the reconstruction of the cosmic star formation rate density up to high redshift. Due to their dust-enshrouded nature, DSFGs are often invisible in the near-infrared/optical/UV bands. Therefore, they necessitate observations at longer wavelengths, primarily the FIR band, where dust emission occurs, and the radio band, which is not affected by dust absorption. Combining data from these two spectral windows makes it possible to characterize even the dustiest objects, enabling the retrieval of information about their age, dust temperature, and star-formation status, and facilitates the differentiation between various galaxy populations that evolve throughout cosmic history. Despite the detection of faint radio sources being a challenging task, this study demonstrates that an effective strategy to build statistically relevant samples of DSFGs would be reaching deep sensitivities in the radio band, even restricted to smaller areas, and then combining these radio observations with FIR/submm data. Additionally, this paper quantifies the improvement in the spectral energy distribution (SED) reconstruction of DSFGs by incorporating ALMA band measurements, in particular, in its upgraded status thanks to the anticipated Wideband Sensitivity Upgrade.