The emergence of orientational order plays a central role in active matter theory and is deeply based in the study of active systems with a velocity alignment mechanism, whose most prominent example is the so-called Vicsek model. Such active systems have been used to describe bird flocks, bacterial swarms, and active colloidal systems, among many other examples. Under the assumption that the large-scale properties of these models remain unchanged as long as the polar symmetry of the interactions is not affected, implementations have been performed using, out of convenience, either additive or non-additive interactions; the latter are found for instance in the original formulation of the Vicsek model. Here, we perform a careful analysis of active systems with velocity alignment, comparing additive and non-additive interactions, and show that the macroscopic properties of these active systems are fundamentally different. Our results call into question our current understanding of the onset of order in active systems.