For everyone who has not read it: Aaron is not proposing the future of ground-based transportation. This is an analysis why he scraps his plans for a magnet-levitation, personal transportation system and a call for new ideas.
So for population densities of 5,000+ ppl/km2 this might work (emphasis on might).
Interestingly, urban areas of the developing world might qualify:
http://www.citymayors.com/statistics/largest-cities-density-...
The problem is that many of these cities might not maintain their high densities as their economies grow. My guess is that a lot of the high density is due to extended families living together. But maybe not, there are quite a few developed world cities on the list (e.g. London, Madrid, Seoul, Tokyo).
Unfortunately, I cannot vouch for the reliability of the statistics presented here, there just a result of a very quick google search. I've got to stop spending so much time on HN.
But, also, in the detailed part of the proposal, he points out that with high densities (e.g. NY city) you need so many maglev cars to meet peak demand, that parking them off-peak is a significant problem.
Because the customer doesn't require a specific car, these parking lots can be FIFO queues or FILO stacks and won't require maneuvering space.
Also, the cars could transition to a much cheaper, non-maglev parking system. This might even be done using a robot to lift and store the car into a slot in an otherwise "dead" grid. One expensive robot that can move in 2 dimensions and a lot of simple steel rails is a lot cheaper than heaps of maglev track.
Finally, the 333k car estimate was based on a subway where there is only one place that people are leaving from. There was an assumption that EVERY car must return EMPTY to the source of the trip afterwards to pick up the next passenger. This is not true, the percentage of returning cars is probably much lower (30%?) And even those cars could be useful for part of this trip.