It was a throwaway line in the episode, but very important: Mon-El says of the prince, very quietly “he wasn’t worth admiring, but I-I want to be.”
That’s what’s behind Mon-El’s sudden “I want to be a superhero.”
Look. He’s the only survivor, as far as we know, of the destruction of Daxam. He wasn’t sent to Earth with a life’s purpose, like Kara. (Who, incidentally, took a while to grow into and cultivate her real one.)
He’s never worked a day in his life before Earth (captain of the royal guard, my eye).
When he says it’s luck that he lived, he means it. In the Pratchett veiw of “worth,” he has none. He’s never had or made any value besides being royalty, never left the world better than he found it, never had a job other than “don’t die.” He’s amusing, but not admirable, as Kara reminds him constantly.
He decides he wants to change that. And Kara’s way, Kara who looks like she knows what she’s doing, it is.