I have several concerns for this concept. First, what city? With that many tunnels underground could make the geo-landscape unstable. However, New York is an example of concept but would have to compete with existing metropolitan transportation. Second, the tunnels would have to be stable against of earthquakes. Lastly, what happens when the skate breaks?

Watching that video I was thinking - why bother with the Telsa cars at all if you have a cheap underground network with self propelled carts?
Also, unless Elon or someone has figured out some much cheaper way to tunnel, tunnels are enormously expensive.
I think having several billion dollars tied up in a car company is blinding him to the use of a PRT system - pods on micro monorail beams in the air. Much cheaper than tunnels or highway elevated roads.
One of the reasons why this hasn't happened yet is that each pod needs to be self driving, and even 15 years ago this would have cost over a hundred grand per pod, even given that elevated pods only have to deal with other computer controlled pods, not pedestrians. Self driving cars may end up largely getting cars out of cities ironically.

@Jim I agree personal rapid transport pods are the best public transport method. We need a standard way to measure transport system throughout like people per minute per square meter. We need game mods that measure competing ideas for city planning transport. The actual best option might be telepresence to better support remote work though. We go through great effort to put people in the same office.

Why bother with this when you could just build an underground railway network with several huge car parks outside the city. That would have the dual benefit of being able to transport many more times the number of people and clean up the city air at the same time. Why be wedded to you cars?

Problem with billionaires driving our future. The tunnel is designed to carry a car with one person on board. Jeez, should it be designed to carry a bus loads. There are other people on earth besides billionaires

May people want to get from one end of a city (straight through) to the other end quickly and a tunnel like this would be fine for an expressway for those not needing to stop in the city. Just passing through. Regardless of the number of passengers in the vehicles, I think a direct tunnel through could work well.

Love the disappearing skates as they lower into the ground below, what happens to the lowly traveler in another mode of transport following behind with the big hole left by the fantasy elevator? Or for that matter when it tries to reappear while something else is moving or stopped on that same ground above it? Just as a reminder, water loves to be at the bottom of all tunnels, so maybe submarines might be in order, unless perhaps planning on running in partial vacuum as well as the Hyperloopy......

Maybe some of us non-billionaires might like to stay solo.

And then there was an earthquake

Or you could move to a place with a lot less traffic. Just saying....