Yes, depth. Kourin is interesting. Consider what we learn about him in CoLA.
On the surface, he seems like a smart guy. His age, along with being a father/mentor figure to the girls, comes with an expectation of knowledge and wisdom. His involvement with artifacts from the outside world lends him an air of mystery, as he's surrounded by things nobody in Gensoukyou understands. And to top it off, his ability to name and describe any object just by touching it makes him seem like a veritable walking encyclopedia. So that's how the girls see him; as much as they may give him a hard time, they do look up to him as an adult and as someone who knows a lot of things they don't. They trust and believe him for the most part, and when he goes on a monologue, they listen.
However, as the series goes on, we the reader discover another side of him, one that should be obvious if you think about it. Who is Kourin, actually? He's the son of unnamed and likely unremarkable parents, born and raised in Gensoukyou, with an ability that led him to a life of collecting and selling trinkets. He's never been to the outside world (well, for more than a couple seconds). He doesn't even live on the mountain, as part of the tengu/kappa society. Actually, he's a total bumpkin. And remember, his ability can only give him the name and function of an object, not even how to use it, let alone its underlying principle of operation. He doesn't actually understand most of the stuff he sells, he can just bullshit about it because that's what he's good at, thanks to his ability. Yes, he does also read some of the books and magazines he collects, but those are random bits and pieces, not enough to really develop an understanding of any subject. He's not a scholar.
And that leads to my point. Kourin isn't a scholar; in fact, he's as ignorant as anyone else in Gensoukyou. It just so happens he has the perfect set of tools to appear smart, so that's what he does. You can see this in multiple chapters, but one in particular that I remember is the one about the fossil.
The girls come to him with a fossil of some huge creature, probably a dinosaur or mammoth, and ask him about it. He starts spinning this tale about how it can't possibly be a normal bone, because the creature would have to be way too big, and there's nothing that big in the world. Instead, he says, it's the bone of some ordinary small creature that became inhabited by a god, making it grow to such a huge size. He goes on and on, giving a fairly convincing explanation. But we the reader know that that's obvious bullshit. We know what fossils are, and that creatures that big did and still do exist. But because neither elephants nor whales nor the study of paleontology exist in Gensoukyou, Kourin doesn't know any of that. He was faced with something he didn't understand at all, and used his vague knowledge of myth and religion to create a convincing explanation for the girls.
That's who he really is. A man who has (at least) two nice young girls who look up to him, and so tries desperately to live up to their expectations, putting on a front of being wise and knowledgeable when he actually probably knows less than them. Just a guy trying hard to be cool.
What you want to take away from that is entirely up to you, but yeah, there's some depth there.