I agree, seems doable. He can hire a bunch of boring oil mining engineers, if he likes. Instead, he wants to reinvent the wheel himself by tinkering. If I had extra money if I were him, I'd get three competing teams: one doing what he's already doing, another made up of oil mining boring engineers, and another starting fresh.
I'm concerned that the collateral damage considerations are different for ocean beds versus urban plots. A super efficient boring machine could expect a certain amount of earthly reorganization, and that could be bad in an urban environment. Engineers would have to do rigorous soil samples, figure out minimum depths and practices to avoid damage to overhead structures, and then whatever necessary reinforcement placed in while the boring machine was proceeding. I could conceive of a sleeve chasing the boring machine to hold up all newly dug material, and behind the sleeve, a permanent structure laid in, with whatever molding forms it would need to let it cure. If cement based materials (such as concrete) were used, I would have to wander over to another problem:
If using concrete, is Elon Musk considering enhancing the cement making industry to be clean? There's enough sunlight to heat up a cement kiln, but it has a serious consistency deficit. Augmenting sunlight energy with other high heat clean energies would be necessary. What could sunlight be converted into for use during darker times that could heat up a cement kiln? One idea I had was making (I know, gasp) hydrogen, and burning that in the kiln. Is making cement from sun heat and hydrogen still toxic to our environment considering the chemical conversions going on during the entire manufacture? A huge amount of concrete would be used in building this new tunnel system, and so far, the only viable energy sources for cement factories have been coal, and a lot of it, with exception of I think one cement factory in the world that uses oil derivatives (usually considered too expensive).
Even better, a superior material to concrete could be used. Have they figured out a way to create carbon fiber inexpensively enough and cleanly enough not to pollute the world during its manufacture? Or, is quartz glass such a wonder material? We know Musk's companies already use a variety of exciting composites; perhaps some material (any kind -- exciting or not, composite or not) is inexpensive, strong and clean enough to use to hold the tunnel in shape.
Ambitious and fun!