Asahina is one of my favourite Danganronpa characters. In this strange, paranoia-inducing situation, she was the first character I came to trust completely. She just seemed like such a normal, well-meaning person!
In a game like Danganronpa, I think it's good to have the occasional character like Hina around. I really appreciated having her friendly presence throughout the game. She wasn't necessarily always reliable in trials (Trigger Happy Havoc's cast were rarely much help in trials, with the notable exception of Kyoko and occasionally Byakuya; Danganronpa 2 did much better at making sure the trials weren't just being carried by a couple of people), but it was nice to know I could trust her not to hurt anyone, at least.
('Didn't she try to get everyone executed?' you ask, to which I say 'shh shhhhh don't worry about it.' It's fine. She didn't kill anyone, so I still feel I was right to put my trust in her. M... more or less.)
Hina really helps to highlight the fact that these characters are, at the heart of it, just ordinary kids who've been thrown into an extreme situation. Even under the pressure of the killing game, most of them don't want to hurt people.
In the end, that's really what makes Danganronpa compelling. If you locked up a group of seasoned killers and told them to kill each other, that wouldn't be nearly as interesting a story! But it's fascinating to do that to a group of normal people - people who really just want to, say, eat doughnuts and swim and spend time with their friends - and see what happens. Who breaks under that pressure; who ends up killing someone? And, just as interestingly, who doesn't?