Run an S-bahn (https://en.wikipedia.org/wiki/S-train) through the tunnel for 10x the throughput of humans for a given tunneling cost. Cars are a profoundly inefficient use of space in a dense area.
The only way an auto tunnel network would solve traffic is by charging a sufficiently-high toll to match supply with demand. Otherwise, in an area dense enough that traffic congestion is a problem, induced demand will lead to congestion:
https://www.aeaweb.org/articles?id=10.1257/aer.101.6.2616
Boring Company tunnels are NOT for cars-only, they do envision public-transportation-like services which will be much better to move between dense areas:
The attractive areas of denser cities do tend to be more expensive than in less built-up areas. But there are plenty of cities that don't have housing prices from hell. Some also have fairly reasonable commuting times by rail although it's always going to take time to get from outside a city into a city.
Furthermore, there are plenty of companies and housing on the outskirts of cities where there are reasonable housing and commutes.
If everyone wants to live within 30 minutes of a Manhattan office, no, then there's probably no solution.
