Don't forget that metros can also go on elevate viaducts for much less money. Underground is the best solution for dense areas, but the elevated is enough cheaper that you can afford to run a metro a long way out into the suburbs - then those become prime real estate to rebuild to mid rises making the entire city denser (assuming zoning allows this)

I would love to see metros in every reasonably sized city but it's going to run into the built in sprawl problem of US suburbs making it very expensive to run lines out to the outlying suburban areas at high enough density to make them viable. Best work around option I suppose is to build them out to the edges of the city and build a big park and ride infrastructure.

I've long thought of the issues with public transit in the majority of US cities as being trapped at a local maximum where we're forced to implement inferior solutions because we're so far into the car infrastructure getting people to abandon their suburban homes to move to a more dense less car dependent urban structure until the underlying shape of cities would adjust to denser clusters again if they ever did.