My serious interpretation is that "prince" here isn't being used literally to describe the son of a hereditary ruler. Elven lives are so long that they can't possibly have traditions associated with a king dying and his son becoming the new king. Therefore I think "prince" means an exceptional elf, not the king but someone worthy to rule.

(A counter-argument: the mail fits Frodo because it was made for a child. A child wouldn't be called a prince unless he literally was one. My reply: hobbits are short but stocky. Armor made for a slender adult elf could fit a hobbit, although it would be longer on him than it was on the elf - a chain hauberk rather than a chain shirt.)