At highway speeds, 4 seconds of following distance is 120 meters.
NYC's least efficient system is block train control, requiring 300M separation between trains.
In 300M you can fit about 66 Corollas, again packed bumper to bumper. That's 66 * 5 people = 330 people, or approximately 1.5 subway cars.
Subway trains are 6 or 8 subway cars long, depending on track and time of day.
With CTBC some platforms can run at 60 trains per hour (30 local, 30 express). That's 8 subway cars every 2 minutes, or approximately 1,000 people per minute.
To move 1,000 people at all with the Corollas you will need 250 * 4.55M of them, or approximately 1.1 kilometres of cars, bumper to bumper.
Unless your trains are going at 10 kph you will have more of a gap than 300 meters if you see a train every 2 minutes.
You should recognise this argument: it's the same logic given for why self-driving will solve everything.
You're not accounting for the space between trains. They will only take up 5-10% of the available rail space because you need gaps between the trains.