Good for it, but in the mean time a car tunnel would still have worse throughput than public transportation (less than two train's worth per day), rely on unproven technology (both for tunneling and moving the cars in a human-friendly way), and almost certainly not be financially viable (without massive subsidies).
Yes we need better public transportation, but there are well-established methods for effecting this. We just need to invest in them instead of Musk's poorly-conceived flamethrower company.