Earlier quoted context omitted.
There’s not much correlation between density and quality of public transit. If you look at a top 10 list of best transit systems, you’ll see medium density cities like Oslo and Helsinki right beside Tokyo and Hong Kong. Or within the USA, compare Miami to Seattle. The only difference is that one city decided to build mass transit and the other didn’t. It’s entirely possible to build an appropriate transit system for…
Past a certain density point probably. It also helps if there's some degree of concentration where people want to go even if the city as a whole is only medium density. However, things get too spread out and it breaks down--including that transit runs on a sufficiently spaced-out schedule that people with a choice just don't want to take it.
Coming from the SF Bay Area, if you miss a train you'll probably have a minimum 15 minute wait (at least at the stations and times I use), often 2-3x more. People run down the stairs to the platform, shove their way in, and often block the doors from closing if they're squeezing in at the last minute (which extends the last minute, making the train later for the next stop.)
Also, "taking the train" doesn't just mean showing up at the train station. It means checking the schedule and timing it so you show up at the right time. I don't just walk from place to place, using the train as a way of getting around as needed. I plan it out. Or I don't, and use a car instead, which everything subtly encourages.
I agree, frequency makes a huge difference in actual practice.