What you are describing is just a much less efficient, worse version of a subway.
I don't think the entire "car tunnels" thing is reasonable either, but this one is wrong. The bottleneck for cars is the inherent interference in the 2-dimensional streets. If you shove them all in a few tunnels right until they get into a low-transit region close to the destination, it would increase their capacity by a lot.
It's also a huge amount of money that is better used some other way. But it has an effect.
One part of the solution is bikes, the other is mass transit. What self-driving EV pods may be able to do is be people mover for the last mile to a mass transit hub. But for individual traffic across longer distance it simply does not scale.