One argument for containing urban densities is that cities need a critical population density to sustain sufficiently available public transportation. However, the question of whether denser cities foster shorter public transport networks empirically is problematic, because real-world transport nets are a product of many additional factors that are presumably not related to urban form. I have recently published a paper in which I adopted a network expansion simulation approach to generate and analyze counterfactual data on network lengths for 36 world cities. To do so all networks are generated with similar expansion restrictions and objectives. Denser cities are found to have shorter simulated public transport networks, regardless of the tested model parameters. This provides additional proof that densities are needed to facilitate the provision of proximate public transport infrastructure, with potentially self-reinforcing effects.
The paper is published here. The GeoDMS scripts to generate counterfactual networks can be found on my github.