Chasing these 'trivialities' is a good thing, imo.

The Busy Beaver game has lead to a better understanding of complexity theory and automata. Also, direct "hands on" work on improving proof assistants and related tools.

Btw, for those who are curious, the Busy Beaver Challenge wiki is a treasure trove of rabbit holes and curiosities:

https://wiki.bbchallenge.org/wiki/Main_Page