It's solving a problem with tunneling that isn't the problem with tunneling. Tunneling is usually a bit more expensive than a Boring Company tunnel but mostly because nobody would build a tunnel that tiny because you can't actually fit anything in it. Sticking the drilling machine in the ground is the expensive part, not the per-mile tunneling; I guess costs can add up if you have to delay to map out utility connections and stuff, and I guess a Boring Company tunnel could be a little more nimble with that just by virtue of being smaller, but I'm gonna assume it's not a huge difference.
Also, apparently Boring Company tunnels don't have basic shit like emergency exits.
Meanwhile, it's the stations that are usually expensive. Like with the Second Avenue Subway stations, which are both obscenely deep and obscenely huge. If they'd gone for shallower, smaller station caverns, that would have knocked off a LOT of the cost of the SAS project.