The barding is not just a perk, but also a punishment. You guys have to look at this in 4 dimensions. You make your chocobo more versatile by skilling it up using multiple skill trees. That is a reward in of itself. By "specializing" your chocobo, you are severely limiting its functionality. To balance this, the barding becomes a consolation prize.

If you're skilling up your chocobo just for barding, you're doing it wrong. However, that being said, if SE were to implement a reset of some sort, it should only apply to chocobos below rank 10 or chocobos who have at least 1 point in a 2nd tree. This would prevent someone who already obtained barding in one line from getting a 2nd set of barding unfairly (everyone should be limited to 1).