Number theory is an excellent example since it was an academic curiosity until it suddenly became very very useful. While cryptography is built on number theory, that earlier research was not done with the explicit goal of developing cryptography. Instead, people took existing math and built new applications around it.

Obviously, it would be nice to fund only things that are eventually useful, but this is virtually impossible to predict in advance so....we fund a bunch of things and see what works. (Also, math is shockingly cheap compared to lab sciences so it makes even more sense to spread the bets widely.)