That's not quite true: by completely splitting car traffic and pedestrian traffic on different levels, you can create a city which is much denser and easier to walk because you don't need large car streets, and at the bottom you don't need pedestrian affordances alongside car traffic. Plus by banning car traffic far away you disincensise car traffic within the city: it's usually easier to walk, bike or take public transport than go to the bottom, get into your car, drive, park over there and go back up.
Louvain la Neuve works on that model, the city is built on a huge concrete slab and entirely pedestrian, with car traffic and parkings underslab.
I will point out the fact that according to Wikipedia Louvain la Neuve has ~30.000 inhabitants and ~30 square Km (12.5 sq mi). It is also 2Km on the longest side. How do you see this applied to New York or London, cities that need it the most?
And why is it better to still spend billions moving infrastructure underground instead of shrinking what's already available to the point where pedestrians get the vast majority of space and the infrastructure only serves the needs of public services?
> banning car traffic far away you disincensise car traffic within the city
I don't know what "far away" means but in reality drivers still go out of their way to drive the car. Think about this: they are willing to spend hours in traffic jams. You think an elevator ride to level -4 will discourage them?
P.S. I'm using info from BC [0] and their vision on this looks a lot like "let have the same traffic as today but on many levels of tunnels". Only the company drilling the tunnels walks away happy. You just pay a crapload of money to hide some of the issues of urban traffic.
Musk's idea basically focuses on moving cars underground if I understood correctly. It should focus on moving most of the public transport underground and simply "decommissioning" some of the road infrastructure from the surface.
That's not the solution if still you plan on having every person and their car move around. Maintaining the infrastructure for cars on the surface is already expensive and inefficient. Suddenly we can do it better or cheaper by multiplying it underground? You won't get rid of any of today's problems except one: drivers will be able to move from one side of a city and create a traffic jam on the other in no time.Tunnels are great if you plan on connecting a few hubs spread around a city. From there you can use the most efficient surface transportation available. A bike, a bus, a tram, even on foot.
One lesson that most city planners learned in time is that the more infrastructure you build for cars, the more cars you'll have clogging it. The solution is o discourage the reliance on cars in cities and it worked every time it was applied.