That is a really interesting question. I would guess that the answer probably varies from person to person (for those who want to find it, that is). Some are probably just curious. Others may want to find it for apologetic purposes. Others may have other reasons.
Since I’m not sure that the ark is still around, I’m not sure that such a venture is worth the time it would take. Additionally, if it were found it might not do a whole lot to advance the Kingdom (though it may have some apologetic value). Apologetically, what I think is more interesting is what the geological record says in comparison with what Genesis says about the flood. If the geological record says that there was no worldwide flood, then what do we make of that? Personally, I haven’t spent a lot of time studying the Genesis account of the flood, but I have heard some scholars suggest that the story is really about a local flood. It would be interesting, if time permitted, to really dig into the flood account, do some exegesis, and see if it is really talking about a literal worldwide flood or not (and if not then what). Also of interest, I would say, is the question of what the geological record actually communicates. The article above suggests that it says that there was no flood, but it doesn’t go into detail.