One has to remember that Spock didn’t want the kind of information about Khan that he could’ve gotten from the ship’s library computer. None of that would’ve been useful in the situation he was in. So, he played the odds and decided to enquire if Spock Prime had ever come across Khan. He wanted the chance to talk to someone who actually met Khan and get first-hand insights into him that would be useful in this crisis. For what he needed, contacting Spock Prime was the logical thing to do.
So, how does that make it unnecessary? Why does that make it only gratuitous fan service? He had a unique resource at his disposal. Why not tap into it? Seems almost essential to the story. In fact, since Spock seemed to finally have a determined plan after his conversation, maybe it was essential.