This question already has an excellent answer from GendoIkari, but I see two separate questions. They overlap considerably, but they also don't overlap entirely.
The title question is "Why is everyone so focused on the black box in LOST?", which morphs in the body of the question into "can a plane's black box be used to locate a missing plane?" I find the original question interesting, and I believe it adds something to answer that, apart from the question it became. To wit:
Characters don't always have complete nor correct information about the world they inhabit. Lots of people believe that things about which they aren't experts behave in ways they don't, or even which would be impossible. And technology is ripe for this misunderstanding.
So, regardless of whether or not a black box can help authorities find Oceanic 815, some of the characters in LOST are obsessed with it because they believe that's something that black boxes can do. Per GendoIkari's answer, they are partly correct, but tragically mistaken on the details.
e.g., Shannon seems to think the black boxes are magical, guaranteeing that they will be rescued so quickly that they don't even need to worry about shelter, food, water, or organizing.
True, this question is tagged with
realism and my answer is all about unrealistic things characters might expect; on the other hand it is very realistic for a story to portray the unrealistic expectations, ignorance, or belief-in-the-face-of-counter-evidence that real people exhibit in real situations in the real world.
A much shorter answer for "Why is everyone so focused on the black box in LOST?" therefore would be : because they are desperate people, in a desperate situation, desperately in need of a reason to not give up hope.