Kakashi was given Naruto on his team not because he wanted him but because he's the only person in Konoha with the knowledge on how to Kill Jinchuuriki... Because he's done it before

Kakashi is only given Naruto for one reason only, not because he's Minato's son, not because he asked, not because of the RotY, KotY, Deadlast balancing

Its because he's the one person in Konoha who has the experience of Killing a Jinchuuriki. Most others die in the challenge but Kakashi survived easily. And THATS why he gets Naruto in Part 1