There's no indication that The Boring Company is capable of meaningful cost reduction in this regard. The actual cost of physical material in constructing tunnels is a relatively small cost of the project (note that most of the cost in a subway isn't the subway tunnels themselves, it's the subway stations). The only meaningful idea I've seen about cutting costs from The Boring Company is recovering TBMs, which strongly suggests there's no sense of why tunnels themselves cost money [1].
If Musk just talked about being able to build tunnels cheaper, even transit enthusiasts would have a hard time bringing themselves to care. But between Hyperloop and his underground road conveyance thingy, it's quite clear that he has no idea how to build any high-capacity transit [2]. It seems as if he cares far more about "how do I get me from A to B most effectively" rather than "how do I get a million people from A to B most effectively," and moreover, that he doesn't even realize that those are different questions that necessitate different answers.
[0] https://www.nytimes.com/2017/12/28/nyregion/new-york-subway-...
[1] TBMs are largely unrecovered because it costs too much to recover them. You can't back them up without risking geological stability of the above ground, and digging a cut-and-cover shaft to reach them is quite expensive.
[2] On fixed-guideway systems, the capacity is largely dictated by station dwell time and switch fouling time, which governs the minimum headway between adjacent consists. Consequently, you need high capacity through consist to get any meaningful capacity. But the Hyperloop pods and the road sleds both envision ultra-low consist capacity, consequently killing total throughput. Incidentally, higher speeds also reduce capacity.