Most of that extra cost comes from the legal fees around buying the land and getting permits to dig under it. A better tunnel borer doesn't address any of that.
You could maybe save on OSHA concerns if you can somehow slash the number of people employed, but you'd need to get rid of a LOT of people before you see enough gains from that to make this a game changer.
Elon's whole deal around transit is utterly uninformed about anything urban planning.
Except it does seem to have addressed that. Even the dumb test tunnel seems to have been completed for far less than it should've taken, given the constraints you mentioned.
Experts (including those who have studied foreign mass transit in detail) are at a loss to fully explain why the US's tunneling costs are so out of whack compared to other countries. Sometimes, when expert systems seem to have failed, it's a useful exercise to throw everything out (i.e. be "utterly uninformed") and learn from scratch by trying. They may fail anyway, but it's worth a shot.
Sometimes, the naive intern will find a solution because of their own naïveté. (And even then there are lots of practical things that will need to be relearned, at great pain.)
I'm under the impression that their costs are cheaper right now because public agencies are eager to see a working test case and so exempted them from environmental clearance. I doubt that will still be the case when the scheme changes from "a single tunnel from Musk's home in Bel-Air to his work in Hawthorne" to "hundreds of stacked tunnels traversing the entire city." But I'm open to corrections.
If they can somehow address the insane tunneling infrastructure costs in the US, I don't really care what path they take to get there.