You know who doesn't like him? Garrosh. But everyone hates Garrosh, and the guy is going to be killed in the end, so it doesn't matter. And besides, everyone just likes Anduin more because of that.
Anduin is also smart. And funny. And important. And handsome. And rich. And powerful. In fact, Anduin is basically what your wife wishes you were. And he's only 15. In any case he's so much better.
That being said, he has his problems. For example, he often has guards. Guarding him. Because, once again, he is a prince. Who is going to become a king. And lead not only the alliance and the horde, but also the dragons. But the dragons aren't enough either. He's also leading the Naaru. But enough about him leading the mythical beings of Azeroth, we're dealing with his problems. His guards. Trained. Elite. Guards. That he manages to slip away from. On multiple occassions. To do things. Like train under the pandarens. Oh by the way, he's learning meditation now. He's going to become a monk as well.
He also has two stories about him. Did you think, when you read Varian and Velen's stories, you were going to read about Varian and Velen? Lol nope. You're reading about Anduin. Did they mention Varian or Velen? Then it's just their thoughts on Anduin, and on how great he is. BTW, do you know why Varian and Velen both have 12 pages to a story each, while Bairne only has 6? It's because Anduin is in their stories. Did I say in their stories? I misspoke, it is because Anduin is their story
Anduin's demons? Growing up without parents. AKA he is basically allowed to follow the path of Batman. However, he had Bolvar. But Bolvar was turned into the Lich King. Coincidentally around the time that Anduin's real dad came back. So he always had a father figure. And not to worry, Anduin is a priest. And is going to be a paladin. And soon a monk. Which means that he'll probably purify Bolvar. And Kil'Jaden. And Sageras. He'll just purify everything. And if someone tries to kill him? Psh he's a hunter. And a warrior. And a priest. And a pally. And a monk. Who leads the most powerful mortal races, the dragons, and the Naaru. Good luck with that.
But that's not all he'll do. Anduin will be able to tank a Saurfang cleave. By himself. He'll also restore the forsaken. And the scourge. And deathwing, nefarian, onyxia... basically the whole black dragonflight. Also, once again, all while purifying Kil'jaden. And Bolvar. And Sageras. He'll also be able to see every tauren rogue in the game. Heck, he'll be able to become a tauren rogue. Why not? He's already a priest, warrior, and a hunter, and is going to become a pally and a monk. He'll also be the first bard. And warlock green fire? He already had that. You just never saw it because he doesn't cast felflame spells. But not because he can't, just because it wouldn't fit his lawful good character.
Seriously, as annoying as Thrall was, at least Thrall had some character development + some issues on where he stood with neutrality and such. The only reason people aren't screaming "Marty Stu" at Anduin is because he's not a girl so people don't naturally think of the term.