How urban characteristics change with total population, their scaling behavior, has become an important research field since one needs to better understand the challenges of urban densification. Yet urban scaling research is largely disconnected from intra-urban structure, and this seriously limits its operationalization. In contrast, the monocentric model of Alonso provides a residential choice-based theory to urban density profiles. However, dedicated comparative static analyses do not completely solve how the model scales with population. This article bridges this gap by simultaneously introducing power laws for land, income and transport cost in the Alonso model. We show that the equilibrium urban structure of this augmented model matches recent empirical findings about the scaling of European population density profiles and satisfactorily represents European cities. This result is however not compatible with the observed scaling power of housing land profiles, and challenges current empirical understanding of wage and transport cost elasticities with population. Our results call for revisiting theories about land development and housing processes as well as the empirics of agglomeration benefits and transport costs.