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Polarization measurements are usually considered as the most difficult challenge for the QCD description of quarkonium production. In fact, global data fits for the determination of the non-perturbative parameters of bound-state formation traditionally exclude polarization observables and use them as a posteriori verifications of the predictions, with perplexing results. With a change of perspective, we move polarization data to the centre of the study, advocating that they actually provide the strongest fundamental indications about the production mechanisms, even before we explicitly consider perturbative calculations. Considering ψ(2S) and ϒ(3S) measurements from LHC experiments and state-of-the-art next-to-leading order cross sections for the short-distance production of heavy quark–antiquark pairs of relevant colour and angular momentum configurations, we perform a search for a kinematic domain where quarkonium polarizations can be correctly reproduced together with the respective cross sections, by systematically scanning the phase space and accurately treating the experimental uncertainties. This strategy provides a straightforward solution to the “quarkonium polarization puzzle” and reassuring signs that the factorization of short- and long-distance effects works, at least in the high-transverse-momentum region, least affected by limitations in the current fixed-order calculations. The results expose unexpected hierarchies in the phenomenological long-distance parameters that open new paths towards the understanding of bound-state formation in QCD.