Why does research on the busy beaver function get funded?
Extremely likely, this concrete example is useless. So is any other concrete example. However, there are many of these examples, and we do not know which handful of them will be useful.

Some ancient people wasted time on research in number theory, some of which ended up being practically useful. Some studied motion of stars in detail far exceeding calendaring and navigational needs. This also proved useful. 

Many, many studies also led to dead-ends. At the time, one could not tell which of them would.