Honestly I thought about this in the past and I have to say that Hitsugaya probably plays a much weaker supporting role than Renji. However, I think that he would be a better character if they explored his relationship with Aizen's former lieutenant which would be relevant and interesting to the main plot and past transgressions that occurred.
I'm not sure that's a bad thing, seeing as Renji's role is to get his ass kicked to elevate the badassness of whatever villain he's fighting. I dunno if his relationship with Momo would go anywhere, she seemed ridiculously shallow as a character (she's spent the majority of her screentime in perpetual lockup or hysterics).
Ikkaku (bald lieutenant) is the perfect example. He only uses his Bankai when none of his teammates are looking. He has a good reason for getting owned and it's a sensible reason for why we rarely see his Bankai in action. It is definitely a ticking time bomb that anyone would be interested to see how it turns out. I am sure Kenpachi would beat him senseless on the spot if he knew that this was the case.
It might be rooted in a sort of understandable logic, but it's pretty arbitrary, and it allows a sort of Renji-ification of Ikkaku. We know he's got X amount of power, but he won't use part of it, so that's an excuse why he got beaten by Y character, but it gives him space to kick someone else's ass or whatever later, since we know he's got it.
The greater problem is a lack of development. Renji at this point is a tool, literally and figuratively. His role is to get his ass kicked. He's not changed or grown as a character for ages, and he's only used to get his ass kicked. And this happens to other characters as well, particularly with having Bankai. It's an outer limit (at least not without going down another path like Ichigo/Vaizards, Aizen, etc.) for Shinigami, and once you get it, it defines what your character can do and that's all they'll ever be able to do. So Renji gets his ass kicked constantly, Ikkaku effectively tries to always pull his punches, and Hitsugaya is the stock captain for pretty much anything involving the real world and so forth. They stop being characters and become more like props just to have fights. But since you know all the moves on their side it gets boring.
Last time I saw him I think he defeated Noira.
Yeah, think so. Standing around in the desert. Same with Kurotsuchi I think too, although I guess they opened Syzael's lab or something? And there's the fourth captain sorta hanging out too I guess.