One of Elon Musk's ideas is that underground you can have a three dimensional system of tunnels and that this can help solve some of the capacity problems.

As dense and as cheap as Musk's technological vision becomes, a question remains: why carry a car at all instead of carrynig people ? Why carry mostly dead weight ? The denser the network, the more acute that question - if Musk's vision is an ubiquitous three-dimensional underground transport mesh, then why does it seem to conscientiously avoid being a public transportation system ? Does Musk believe that saturating the city with autonomous vehicles that use tunnels as network backbone can be more efficient than heavy public transportation networks ?

Because Elon owns a car company. That's fundamentally why.