Has anyone had their ESTA application turned down because of their age?

Going through customs and immigration with that chip on your shoulder will surely make it a much more lengthy and uncomfortable process than it need be. It is better to show up at as a guest anywhere without such an attitude. Remember, you will be a guest in the US, they do not have to let you in at all. If you are traveling under the Visa Waiver Program, they don't even really need a reason and you have no recourse.