I have previously suggested that it is inevitably more complex than that. First, it is misleading to characterize whole metropolitan areas by their overall density because that masks considerable variation within areas. Second, we know that there are successful clusters in high-density Manhattan as well as much lower density Silicon Valley. Path dependence is powerful and we do not expect either place to evolve so as to become like the other.
I have just read "Travel and the Built Environment: A Meta-Analysis" by Reid Ewing and Robert Cervero. The authors survey the many elasticities that various researchers have estimated. They admit right off the bat that, "Surprisingly, we find population and job densities to be only weakly associated with travel behavior once these other variables are controlled." I am not surprised.
One meta-finding (of many) is the elasticity of vehicle miles traveled (VMT) with respect to household or population density (their Table 3) which they report is -0.04. This is very small but, for practical purposes, what does it mean?
New development occurs mostly at the fringes of metropolitan areas but there is also considerable "infill" development. In most cases, there will be pressures to develop the project at a higher density in the name of less VMT. But there are two problems. First, more people traveling a little less could still generate more overall VMT. Second, if the higher density leaves more space available, would the space be developed? If so, we get even more people and more VMT. If not, the space will have to be traversed by anyone going to or from the new development, creating more VMT. Simple rules are never adequate.
New development occurs mostly at the fringes of metropolitan areas but there is also considerable "infill" development. In most cases, there will be pressures to develop the project at a higher density in the name of less VMT. But there are two problems. First, more people traveling a little less could still generate more overall VMT. Second, if the higher density leaves more space available, would the space be developed? If so, we get even more people and more VMT. If not, the space will have to be traversed by anyone going to or from the new development, creating more VMT. Simple rules are never adequate.
That aside, Google scholar yields 39,800 hits for the paired words "density" and "sustainability" since just 2009. A small sampling of these involves studies or tomes that link the two in a positive way. That suggests yet another meta-study.