Density is not a panacea though. Density reduces revenue per capita as you end up with property tax from the cheaper housing so as you build it you see declines in services. Most notably education, if you ever wondered why suburbs tend to have much better schools than urban areas a big factor in any jurisdiction where schools are paid for in part through property tax is that the suburbs have more property tax per student.
Roads are also an issue as it is seldom viable to build more of them and there is limited ability to widen the ones we do have. The net result is a substantial worsening of transit infrastructure to levels far worse than ever intended for those neighbourhoods.
Property taxes can be raised, if higher density makes it so that existing taxes are too low. Furthermore, education is more strongly correlated with parental education and involvement than with spending per pupil. Wealthier, more educated people tend to live in suburbs, that's why schools do better there.
Higher density makes mass transit systems like subways more viable, opening up alternatives to automobiles. Furthermore, greater density means more revenue to spend on infrastructure projects.
When a metro area experiences growth, higher density is inevitable. It's more a question of how that density will be accommodated. Construct no housing and it will take the form of ever-increasing home costs, and higher rents for increasingly subdivided apartments. Construct denser housing and people will be able to live comfortable and affordably.
Roads are also an issue as it is seldom viable to build more of them and there is limited ability to widen the ones we do have. The net result is a substantial worsening of transit infrastructure to levels far worse than ever intended for those neighbourhoods.