They are able to recoup some of the costs by using the waste material to make bricks on-site. They could give the bricks away for free and it would still work out cheaper (as trucking waste away is extremely expensive). Anyone could obviously do this, but Boring Company currently has the pipeline set up to do it.
They use an electric train to move the waste away underground. This comes with many benefits - including eliminating the need to drill ventilation shafts for workers (which cost time and money).
If you're not receiving federal funding for the project, the cost is pretty important. The Boring Company can likely do things cheaper than anyone else.
Raw drilling speed isn't the only area where innovation is occurring. I'm not sure if their biggest optimization (cross-section area) applies here, because the type of vehicles in the tunnels is a factor in that vision.