The problem is that she's not even really rising to greatness. She's a terrible ruler, but she has dragons. That's apparently what her arc was all about. She shouldn't rule jack shit... but, dragons.
Obviously yes, But she is learning and her character has been considerably developed in season 4 and 5.
And yes, her control of dragons is a metaphor of her controlling the the world around her. The moment she started to lose control over her children all hell broke loose, now she summoned AND tamed drogon. Dany is back yo!