In The Golden Bird, the king is convinced that his youngest son is not up to The Quest, and indeed, "if a mishap were to befall him he knows not how to help himself; he is a little wanting at the best." — which leads naturally enough to his success.
Many Russian Fairy and Folk Tales have the main protagonist, named Ivan the Fool (Ivanushka-Durachok is the endearment for him) who fits this trope perfectly. He starts as the village idiot and lands in some incredible adventures. Sometimes he transforms into a handsome and non-foolish prince at the end of the story, and sometimes he refuses the fortune, the Czar's daughter in marriage, and the transformation, to go back to his original village idiot occupation.
Puerto Rican folk tale character Juan Bobo (literally "John Fool") was one of these or Book Dumb, depending on the tale. Sometimes he was stupid enough to kill his own baby brother while babysitting him; other times he got the better of people trying to take advantage of his naivete.
In some variants of The Love of Three Oranges, the prince is a fool, which is how he gets himself cursed, and is foolish enough to waste the first two oranges.