That's a very deep question, especially for those of us who celebrate Konno Day every day. Long post (essay) ahead.
Back a little over a couple years ago, I was just starting out with getting to know H!P, I wasn't familiar with 5th generation, so I was a Rika fan. The Peace, All for One PV, chickens, very pretty, cutesy voice, etc etc etc... In all, mostly for superficial reasons. (Though she does have a killer body and a smouldering look that can melt the screen.)
My first exposure to 5th gen as a group was through Ayaka's English Lessons. Previously, all the other members had some reluctance to cooperate, but not this one girl. She seemed like she was more polite and reserved. In a word, "demure". I always liked that kind of girl over the more go-go-rah-rah type. (Sailor Mercury > Sailor Moon for example) As one raised to appreciate good food, I could also appreciate how much of a gorumet she is.
Later I watched the Bakajo test. Konno got major points in my book for coming in first. With her status as (arguably) the most intelligent member, she had a new spotlight cast on her. I got the impression that she was the kind of person that does things seriously and capably, despite being a little spacy at times. When I got to the 13nin Gakkari Christmas special, watching her manipulate all the other members and bend them to her will, I couldn't help but smile. Plus, learning about all the difficulties she faced was really endearing.
It wasn't long until I started looking for her in performances. While all the front girls may have had more conventional good looks and better voices, Konno had her hard work and constant effort. Being such an unseen supporting force in Morning Musume made every time she had a closeup into a little triumph.
Somewhere in there, I saw the Momusu vs Bob Sapp video. In the balloon popping game, you can see Konno sneak up behind him and pop one of his balloons while he's distracted by the other girls. With all the other girls running around and screaming, that was just about the only strategic action in that game. And it was by the ever-capable Konno. And of course, in the second half, she just owned The Beast at that pattern matching game.
On Hello! Morning during that fake food game, you could see the pressure Konno puts on herself. If memory serves, not only did she have to go last, but if she messed up, none of the others could eat either. In the slow buildup to her turn, you could see the anxiety mounting. When she started crying, you could see just how hard on herself she is. If any of the girls needed support, this was that girl.
And supporting her is what I tried to do. At this very moment, all 5 of her PBs are right next to me. I own no others. The girl has a way with the camera that makes you feel like you're right there. I guess it's partially her huge, expressive eyes. The fact that she's got some meat on her bones and a nice figure didn't hurt either.
It's been said that Konno fans are some of the most fanatical. This doesn't surprise me at all. It might sound a bit cheesy, but Konno, as the hard working, "spare" underdog, has come to represent personal redemption and hope. To believe in Konno, and her efforts, is to believe in the ability to improve one's self and the ability to defy others' expectations. How many other members could you say the same about?
Sure, there's lots of superficial reasons to love Konno. But they're by no means the only reasons.