True commuter rail, that runs primarily well-loaded trains at rush hour, is by and large a win, both from a congestion and energy standpoint. Some commuter rails don’t even run empty reverse trains, they just own enough trains to have some decent fraction of them come in during the morning, sit and go out at night.
Commuter rail though, does not increase residential density that much. People tend to drive to the commuter rail parking lot. The rail makes it easier to suburbanize, not harder. But it does reduce congestion and does save energy. It, and certain long-haul (amtrack) are the most efficient trains there are. I would venture most commuter rail riders own cars, though they may own only one car for a couple thanks to the commuter rail.
Transit, as a true car alternative, can’t run at just rush hour, and this is the rub. It has to run all those light load, heavy vehicles and it has to run them to the end of the line and back. This is what curses transit with those poorer than expected energy numbers. It’s real hard to fix. To fix it you have to get people to not own cars and take their mid-day trips by transit. Which they do in some cities (like NYC, and much more in Asia and Europe.) But even in those cities, the improvement over cars is less than people imagine, and in fact small city cars (lightweight, electric) and scooters will be more efficient, without offering the negatives of transit.
In U.S. cities, transit faces a curse. Once a person decides they need a car for some fraction of their trips, they buy one. Once they have a car, they now have a reason not to use the transit, as they view the cost as only the incremental cost of gas and parking, the vehicle already being paid for. Indeed, it is wasteful of all that money to take the bus.
A hard reality is that while almost all transit systems are designed hub and spoke, a large fraction of trips in cities are not to and from downtown, and these are the trips that make people decide to buy a car.
One answer to this (New York’s answer) is the taxi fleet. In NYC you don’t need a car because, for those trips that transit can’t do well, you can always get a taxi. This prevents that curse.
Of course my prediction is that in the 2020s, robocars can completely rewrite these rules. Fast, private, efficient, uncongested, door to door, no-parking, no waiting, non-stop, anywhere to anywhere. Commuter rail will survive for rush hour but otherwise it’s hard to see much to keep the other lines alive. (Well, uncongested takes a bit more time as humans will keep driving for a few decades more, perhaps until they start being billed for the congestion they cause.)
You say “transit supports density” but of course some people like density and some don’t. Waves of parents of small children starting in the 50s fled density in spite of the high cost of cars. They saw many downsides to density, which beat out the upsides.
But we live in a very different world now, and with much smarter computers. We are well within the grasp of allowing many forms of transportation to work with many different densities. People will buy and vote for the densities they like. The reality is that the young and childless tend to value the entertainment value of city life, and the parents tend to assign far greater value to yards, detached houses, low density, safety, school quality and other things their children will encounter. No reason higher density can’t have good school quality, and even safety but that’s not the current trend.