Can someone please explain Nidalee to me?

I mean, I know why I play Nidalee - because it's fun to shapeshift into a cougar and leap at people. I also enjoy the skill of landing spear shots and having some minor healing/buffing for teamates. I picked the champion based on my personal tastes for what would seem fun. But after playing her I don't understand why anyone would pick her in terms of being useful. It seems like when facing any other champion (that hasn't fallen way behind, or isn't a bot, or that doesn't have all of their abilities at the peak of cooldown), I can hit them with every single thing I've got and I still die. For example (and this is just one example of many), Kayne walks up to me, he is 3 levels below me (I'm lvl 11, he's lvl 8 - and he has 0 kills). I hit him with my spear, buff myself, turn into cougar, leap and hit him and land my other two cougar special attacks. He proceeds to kill me with about 40% health left for good measure. So I guess I don't understand why other characters have to be so much more powerful than Nidalee. I've read old threads about this and people tend to say, "you just need to learn how to play her" but I don't understand what that means if I'm not missing shots, I'm hitting them with everything I've got, even catching them by surprise, and then they just look at me and I die. It's difficult to even hit people with the spear and I understand the high-risk high-reward thing but it really feels like there's very little reward when everything goes right and I still don't even come close to killing other champions. Now there have been cases in very late game when I've gotten a ton of Ability Power items and I can do good damage with my spear and then kill fast enough to not be obliterated before I can finish them. However, these were always situations where my whole team was so far ahead and the enemy was distracted by my teammates that while yes it was fun to pounce on them it wasn't really that helpful. So why wouldn't I for example just be Lux where I can hit more often with my AoE blast and do great damage and just finish people off at a distance without risking my neck every encounter? Anyways, sorry if this got ranty but I really am open to someone to explaining why to pick Nidalee over other champions.
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