Many "open problems" in mathematics are not actually that interesting on their own. Take the Collatz conjecture: it's pretty much just the statement that a certain 3 line program terminates. In many cases such as this, it is not the truth or falsity of a statement that interests people, it is the method to arrive at a proof which yields new insights.
For example, the graph minor theorem states that a certain order on graphs does not have an infinite antichain. Classically this may have some interesting consequences, but in reality it's not very useful. However, the proof contains some real gems, such as the notion of tree decompositions and the graph structure theorem that lead to mountains of new results all throughout graph theory and related disciplines. Tellingly, the graph minor theorem is a short and simple question while the graph structure theorem is a deeply technical statement that would not have been conjectured on its own but rather was discovered in the process of showing the graph minor theorem.
For example, the graph minor theorem states that a certain order on graphs does not have an infinite antichain. Classically this may have some interesting consequences, but in reality it's not very useful. However, the proof contains some real gems, such as the notion of tree decompositions and the graph structure theorem that lead to mountains of new results all throughout graph theory and related disciplines. Tellingly, the graph minor theorem is a short and simple question while the graph structure theorem is a deeply technical statement that would not have been conjectured on its own but rather was discovered in the process of showing the graph minor theorem.