Light rail and subways are key to effective public transportation and affordable connected cities. Buses are best for last-minute/first-mile transport.
Commoditization of tunnel boring technology around a couple standard sizes for any soil condition would radically reduce subway construction costs around the nation. That same technology could be leveraged for commercial transportation as well.
I strongly suspect "tunnels for cars" is just marketing. Elon is known for doing his research, and the research shows that traffic is reduced by getting people off the road... Traffic is the equilibrium of convenience and discomfort, adding roads just puts more people on the road.
Making mass transportation more convenient and cheap is vital to reducing traffic... the other piece is zoning for high density to support mass transportation.