I don’t think there HAS to be but I get it if people want that. I think ‘Fighter’ has enough narrative flavour for me to take any power and bake it into a story and make it fit the setting I’m playing in. Being so good at something (like acrobatics or athletics ) as to be the rare person who ‘unlocked’ the secrets of flight seems a perfectly good justification for a power. (Just as an example since it was used several times). It seems just as plausible as ‘blood of a Demi-god’ but I see the former is much more proactive (practicing and becoming renown for it) while the latter is passive ‘background’ fluff.
There has to be a default flavor, from a reallife marketing point of view.
There are many players (including DMs including me) who want to create their own flavor. So the default flavor needs to be innocuous and easy to remove and override.
That said, many other players (and probably numerically greater) feel it is the designers job as an author to supply a rich and flavorful world. In the interviews, the designers themselves often mention the importance of "narrative" when deciding if a concept justifies an addition to the mechanics.
The other day I was looking at a chart that showed the result of an informal survey. It was contrasting how good the mechanics of each subclass is versus how fun the subclass is to play.
There was a direct correlation between how mechanically effective something is and how fun it is to play.
The only exception to the direct correlation is, somethings can be acknowledged to be mechanically effective but still unfun. There were no examples of something fun that is ineffective.
My takeaway from it is. Fun flavor must have mechanics to support it. But good mechanics can never be a substitute for fun flavor.
The DM can invent new flavor that the players enjoy. But there can never be a vacuum in flavor.
If a Fighter does things that are overtly superhuman, a flavorful explanation needs to fill the vacuum.