We don't need him to decode but to make perfect copies of the notes since if the tower's records can be destroyed beyond recovery we have the only source of Leaf intelligence dossiers, reports, etc.
Single points of catastrophic failure are bad and Hazou is in a unique position to fix this problem.
This is a good point: Kagome is the only one who can decode this in our clan and Asuma did defer to allowing Kagome to go on the mission before having him decode the notes.
Ideally, this means that decoding the notes isn't time sensitive despite us just being told it should be our top priority.
However, it's possible that the bridge is more time sensitive than the notes so we shouldn't just wait for Kagome to come back before we try to decode them somehow (perhaps by asking if Asuma would be willing to have Tsunade and/or Oro look through the notes to see if they can help since they knew Jiraiya since they were all kids?).
It's less about expecting our boss to be reasonable and more about demonstrating our initiative and patriotism. Our leader just told us he needs these reports ASAP for the good of Leaf. Telling him that we will get to it after tea time sends a lackluster message WRT our loyalty to Leaf and its needs.