What pushed kennen and Jayce into the toplane meta and effectively made them stape picks at worlds was the buffs they received prior either through changes directly to their kit (
's mana cost and ratios) or the release of new items
. It's arguable that Kennen's kit is fairly healthy on its own due to having actual counterplay through a situational stun.
Nunu's and Illaoi's kits are both binary and primarily offer little utility in team fights. Illaoi's kit is polarising in that if she isn't totally countered she becomes incredibly strong or if she is countered she is utterly worthless. Nunu is similar in that he is either a really good counterjungler, or objective controller, or a total burden to his team. Recent buffs see him as one of the best jungle picks currently.
If you asked a lot of players Nunu's role in a team before his buffs was to make another champion just as bad as he is through perpetual annoyance simply because he isn't exactly the most useful champion in terms of combat. They didn't say this because he was underpowered although for a long time he really was fairly weak.