I agree it is difficult to quantify the costs, but I wanted to get an idea.

A quick analysis shows that while a system like BART may operate at a loss of about one dollar per trip, that is not far off from the costs of operating our car and road network. Based on average fuel economy, and road expenses the state of California subsidies driving at a rate of about 6.2 cents per mile. I didn't find any hard sources, but a few references that the average commute may be about 12 miles. That would make the average subsidy for a commute to be about $0.75.

- BART looses about a dollar per trip: (https://www.citylab.com/transportation/2015/06/how-much-mone...) - California gas tax covers 22.7% of road costs: (https://taxfoundation.org/gasoline-taxes-and-tolls-pay-only-...) - Average fuel economy is 23.6 miles / gallon in the USA: (https://www.washingtonpost.com/news/wonk/wp/2013/12/13/cars-...) - The gas tax is 48.6 cents per gallon.

Math: - Total road expense per gallon of gas sold: 0.486/0.227 = $2.14 - Subsidy: 2.14-0.486 = $1.65 - Per mile $1.65/26.6 = $0.062

Hong Kong, Japan, Taiwan, and Singapore would very much like to disagree with you:

https://en.wikipedia.org/wiki/Farebox_recovery_ratio

Even the London tube does pretty well by this measure.

>I haven't read of a public transit system where the fares covered the costs of building and operating it. I have read that MTA (NYC), BART(SF), Amtrak[1], NJTransit, and other US ones definitely are in the red year after year.

In all of those cases, the fares plus gain in property values far exceed their costs. Indeed, every one of those authorities realizes that it would be net money loser on the sales/property/business taxes generated if they could stop paying maintenance and shut down the transit systems for free.

[1] Edit: except maybe that one.