It is thanks to his jealousy that the Frog becomes the sole singer at the end of the poem.
He envied the Nightingale's talent and therefore tricked the Nightingale into practicing so much it died. After the Nightingale's death, the Frog became the only (and therefore best) singer. The Frog's success was only possible due to his jealousy. If he had not been jealous of the Nightingale, the Frog would not have become the singer he became.
