Not only are there tales where the oldest kid is the hero or the heroine -- "The Thirteenth Son of the King of Erin" is in fact the oldest, in the Brother Grimms' version, the oldest of the "Twelve Dancing Princesses" marries the heroine, and there's a Russian variant of "Iron Hans" where only the oldest daughter is old enough to marry, so she gets to choose the hero -- but there are plentiful tales where they do even better than that and get happy endings without as much pother. There's an Italian version of "Puss In Boots" where all the sons are stuck with a meager inheritance, the older ones getting a donkey and a rooster, and both make their fortunes with them. And you get things like "Rags and Tatters" where the princesses have to marry whomever picks up a flower from the street, and the older ones get a prince and a nobleman, or "The Black Bull of Norroway" where each of the girls goes to get her fortune:
In Norroway, long time ago, there lived a certain lady, and she had three daughters. The oldest of them said to her mother: "Mother, bake me a bannock, and roast me a collop, for I'm going away to seek my fortune." Her mother did so; and the daughter went away to an old witch washerwife and told her purpose. The old wife bade her stay that day, and look out of her back-door, and see what she could see. She saw nought the first day. The second day she did the same, and saw nought. On the third day she looked again, and saw a coach-and-six coming along the road. She ran in and told the old wife what she saw. "Well," quoth the old woman, "yon's for you." So they took her into the coach, and galloped off.
The second daughter next says to her mother: "Mother, bake me a bannock, and roast me a collop, for I'm going away to seek my fortune." Her mother did so; and away she went to the old wife, as her sister had done. On the third day she looked out of the back-door, and saw a coach-and-four coming along the road. "Well," quoth the old woman, "yon's for you." So they took her in, and off they set.