Look, if you tell me that this is just an interesting problem, I'm happy to hear that. If it helps prove some exotic theorem, I'm happy to hear that. I'm also happy to hear that this has a direct application somewhere.
I just want to know.
I just want to know.
That's the reason why you were pointed to Hardy's Mathematician's Apology. He was talking about how his works would never have a practical use.
It turns out he was wrong, because Computers are mathematics made flesh. All these abstract notions suddenly had a practical use.
There is something fundamental about the limits of computing so there might well be something that can be made of the BB function but at the moment it's just pure maths.