I had to make one last point before I stop for the night, which is this:
This is after Kaito has already gone and flown off. This is Hakuba accurately spelling out what Kaito did at the start of the case.
Gosho didn't even bother with re-drawing it. He probably just copy-pasted that part of the file.
The reason I'm stuck on this, though, is that, well...
Shinichi can take Kaito's tricks apart, and predict what he'd be planning to do, to the point that Kaito's aggravated by it.
Hakuba knows how Kaito's head works enough to be able to figure out what he'd have been thinking.
Shinichi can understand how Kid plans things and works, but Hakuba can understand Kaito.
Which is to say that Hakuba's able to pay attention to Kaito-as-Kaito, but also, he's willing to, as well. Shinichi doesn't seem to feel the need to, since that part won't solve the heists, but Hakuba - who, remember, makes a big deal out of asking why do you do that? - understands Kaito's motivation as a person.
Which isn't to demean anyone, because if they all noticed the same things they wouldn't be different characters, and I think that for Shinichi, seeing things from the criminal's perspective and not demonising them can sometimes be something he needs to work on and is part of his actual character development in-universe, whereas that's Hakuba's strength.