The equivalent of BART in Paris (RER) has 90 seconds intervals between trains in peak time - and thats the regional train system, not the metro. It carries 50k pax per hour in each direction - that would be a lot of cars, like eleven cars a second at 1.2 person occupancy.
You mention "cheap tunnel boring" - maybe that is the keystone of Musk's plan that will change the paradigm... With a little knowledge of tunnel boring I fail to see how to disrupt its crazy complexity, especially in urban environments whose density extends underground already: in my neighborhood (La Défense business district) a whole new station is being build wholly under existing construction and interconnected to existing subterranean works, without any disruption - insanely good engineering and insanely expensive.
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 ?
You mention "cheap tunnel boring" - maybe that is the keystone of Musk's plan that will change the paradigm... With a little knowledge of tunnel boring I fail to see how to disrupt its crazy complexity, especially in urban environments whose density extends underground already: in my neighborhood (La Défense business district) a whole new station is being build wholly under existing construction and interconnected to existing subterranean works, without any disruption - insanely good engineering and insanely expensive.