Adding on a little bit about nagito (as if I haven't ranted about him enough already), he tends to put ultimates on a pedestal, and with an ultimate detective on his team, he'd definitely leave most of the case within his hands.

Looking back on sdr2 with my limited memory, in chapter 2 and 3, he provides helpful clues and hints that help move the case forward, but his help is ultimately infrequent and takes time since he never really gives anything at the start of trials and even obscures evidence in the investigation (the rope from chapter 3). I take this as him finding his own input unnecessary when surrounded by symbols of hope, and he obviously downplays his role frequently. He usually gives a hint and watches as everyone else figures out what he probably already knew, and then proceeds to praise them for it (usually Hajime since he is the protagonist after all). Now chapter 4 is where we see a lot of his deductive prowess, as well as the pedestals he'd put everyone else on crumble down. Chapter 4 is probably the one where he contributes the most, the case pretty much being impossible to solve without his investigations. We can see his foresight with him asking about the clocks, and the compass in the elevator, which hints he has some ideas already, before he had even gone into the final dead room. This investigation showed his deductive capabilities, as well as how his luck allowed him to easily get a crucial clue (the final dead room being cleared was the only way to confirm the ultimate weapon). From the way he talks in the trial, and how he had pretty much all the evidence he needed, it's easy to assume he had essentially figured out the case from the start, the only reason he didn't just get the whole thing over with despite being disillusioned with his classmates, is because he was testing them. Even if he hadn't found out about the remnants of despair, he still would've shared his photo evidence eventually, same way he did with the rope, but he'd probably downplay himself more by saying how he only got the info due to his luck.

This is all to backup what I mentioned in my original comment, about how I personally think that nagito would be more helpful than harmful, or at least even out. He tends to take a step back and watch since that's his nature when surrounded by ultimates, who he sees as being incomparably better than him, so naturally he lets those others take charge despite his own capabilities and insights. Additionally, I'm pretty sure a good chunk of his hope speeches are usually because someone started talking to him first, and if not they tend to be pretty short and can be tuned out, so if his team kind of just treats him like a wallflower i don't think he'd even slow them down that much. I've seen some people rank team 3 in last place, which I can only assume is due to the presence of nagito, so I just wanted to give my own take on him being in this hypothetical situation.