Faith is faith. I don't want objects; we all die with nothing.
I don't think the focus is on recovering the Ark as a faith-object but the repercussions that would have upon Jerusalem, Israel, and the entire world. If the Jews found the most sacred object of their religion, it would be earth-shattering. How would you house it and accomodate visitors to it? Would you want the Moslems to continue to occupy the Temple Mount where the Ark should be housed?
This is for the Jew, God still has a few promises to fulfill, and He will.