Go tell me how many conjectures have been proven over time....

It's only useless to study a conjectured if their never solved, and since we can't look into the infinite future it's only solvable if we learn how to send messages back to the distant past we can never tell if it gets solved or not.

With that said, theirs a lot of conjectures that wouldn't help anyone if solved, so maybe pick the most useful ones at first like P=NP.