Big Bertha is roughly 25x the size of boring company's tunnel borer. And, while your math it totally wrong for Big Bertha, it should be 0.5 miles/yr. But if you account for the 2 years that it wasn't running for repairs then it does end up at roughly 1.3 miles/yr.
Why not compare against a tunnel borer of the same size?
The world's fastest tunnel borer of that size was for the tunneling of the blue mountains (described here: https://www.therobbinscompany.com/the-worlds-fastest-tbm/). That was more than 25 years ago and even at it's average speed over the whole project, it was doing 1800ft 4 times faster than Boring company's "amazingly fast" borer.
If there's something special about the Boring company (unlikely) it's definitely not its boring ability. They just buy a used boring machine and they don't even have the expertise to do anything interesting with it.
They are currently building their first prototype. It seems correct that you would build a few tunnels using conventional equipment to gain experience before setting your sights on improving the state of the art, or is there something I'm missing?
You are missing something: the companies that build tunnel boring machines already have engineers who know how to make the machines looking into the problem of making their designs better. It isn't clear that there is a significant improvement available.
Rockets were a small enough niche that there were improvements possible if someone invested in them. It isn't clear if such improvements are even possible. (meaning they might be)
Right, but existing boring machine manufacturers don't have an infinite money pile to burn through, so they can't afford to try all the things that TBC will be allowed to try simply because Silicon Valley will afford them a bottomless pit of cash (until the next recession).
Why not compare against a tunnel borer of the same size?
The world's fastest tunnel borer of that size was for the tunneling of the blue mountains (described here: https://www.therobbinscompany.com/the-worlds-fastest-tbm/). That was more than 25 years ago and even at it's average speed over the whole project, it was doing 1800ft 4 times faster than Boring company's "amazingly fast" borer.
A more typical example boring through very hard rock does ~700 ft per month: https://www.therobbinscompany.com/midhalton/
Or how about a larger tunnel w/ 160gal/s of water inflow doing 1600ft in a month: https://www.therobbinscompany.com/gerede-breakthrough/
If there's something special about the Boring company (unlikely) it's definitely not its boring ability. They just buy a used boring machine and they don't even have the expertise to do anything interesting with it.