Low-entropy motional states of ion Coulomb crystals are an essential prerequisite for a plethora of applications and are typically prepared by laser cooling. As larger crystals are operated in the quantum regime, it remains unclear, and has recently become debated, whether increasing the ion number can be beneficial for cooling. Here, we investigate theoretically and experimentally many-ion sideband cooling and the role of collective effects in different spin–motion coupling regimes. For weak coupling, the many-body effects are insignificant. In the strong-coupling regime, however, the spin and motional subsystems undergo a coherent state swap, enabling cooling by a suitably timed laser pulse. Using planar Coulomb crystals with up to $91$ ions, we demonstrate that the residual mean phonon occupation after one such pulse scales as $1/N^2$ with the number of ions. By iterating the pulses, we measure mean phonon occupations $<2\cdot {10}^{-4}$. For large crystals in the coherent regime, we further show that the spin–motion dynamics becomes largely independent of the initial phonon statistics. Through spin measurements, the state-swap mechanism can be utilized to probe the phonon distribution in the mode.