>One problem is that trains only move an insane amount of people that are all going the same way. Another problem is that all those people have to walk to and from the end station. A "packet switched" system of sending individual cars at high speed solves both those problems, and going just by my gut feel, should have a quite high throughput too.

People are walking from the station to these giant office towers in central London. The walk from the Tube station to the office must only take 5-10 minutes, total. My gut feeling says the throughput won't be high specifically because you'll have 800 or so people trying to get out at the same place at roughly the same time.