Any sort of tunnel construction in the United States has become notorious for taking longer than initial projections and with big cost overruns, so innovation making tunneling more efficient is always a good thing.
That being said, I'm still skeptical of how all this will pan out because of Elon's ideal use for tunnels. As far as I know he's still essentially making them single-lane tesla-only tunnels, which effectively is just like adding another highway lane to increase car traffic capacity. While this tunneling method may be a significant cost improvement over traditional tunneling methods, it's still way more expensive than adding a lane to an interstate and has the downfall of serious capacity restrictions since only cars can use it. Building a 29 mile underground transportation loop to hit all of the big tourist spots in Las Vegas has some serious potential to be very popular and useful, but it won't succeed if it's filled with cars instead of trains.
As for tunneling in Nashville, I don't think we'll see very many tunnels ever constructed here regardless of use. Getting through the bedrock is incredibly difficult and expensive - I would be surprised if the methods Elon's devised to work in the desert would also work here. He might be able to come up with some methods that make tunneling here efficient eventually, but I would suspect that would be years (maybe decades) from now, if at all.