Why is that in any way obvious? It violates the basic concept, and as you say yourself it moves the character into a wholly different concept that is already served.
It's obvious because that's how classes are designed - you have stuff that everyone can do, and everyone can do that, and if you want to do stuff that nobody else can do, then you have to balance that somehow. If you don't sacrifice any of your generic power in order to gain exceptional abilities, then you end up better at that stuff than anyone else.
It sounds like that isn't what you want, though. You want someone who
does have extraordinary power, but doesn't
seem to. That's a much different question, and I'll try to address that in a subsequent post.
This is a sort of character that occurs a lot in fiction, usually in the form of a comic sidekick. It's a character which it seems the whole world could best, but which - when the chips are down - always comes through. Currently there is no way to play that character using any D&D rules set I'm familiar with. Since it is a wholly appropriate fantasy archetype, that's a hole in the rules IMO.
In the vast majority of fantasy worlds, luck isn't a real thing
within the world. Most fantasy worlds operate by internal causality, such that luck is a non-factor to anyone paying attention. Most of those comic sidekicks
should be dead, and
would have died many times if the author had not intervened.
To paraphrase Dumbledore,
The Lord of the Rings is not a realistic depiction of a magical war. John Tolkien never actually fought any Dark Wizards. Real life is not like stories.
In the rare occasions where luck can be quantified
within the world, it leads to even more ridiculous situations, and you end up with something more akin to Discworld than anything else; any world where luck is tangible and quantifiable would have to be
significantly more fantastic than even the highest of high fantasy.
Tolkien isn't stuck for a solution and coming up with things because he's written himself into a corner. Tolkien is crafting the story this way on purpose to make a point. The armor the hobbits have - their basic decency, their humility, their courage, their tenacity is going to serve them better against the real threats they face than Boromir's prowess at arms. That's the point of the story. The point is that the real challenges of life aren't things you can just swing a sword at.
Then it's an escort mission, the power disparity is real, everyone acknowledges the power disparity, and you bring them along for moral guidance. If you try to set up the rules of the world such that the hobbits - thanks to luck and whatever - are just as good in a fight as a Fighter, or just as good at exploration as a Rogue, then you're entirely missing the point that they're special for RP reasons in
spite of not being good at fighting or exploring.
Of course, the Stormwind Fallacy still being a thing, there's not much reason why anyone would want to RP a weak character if they could RP a strong character to the same effect. In a D&D world, which doesn't follow storybook logic, a hobbit is a liability who will get everyone killed, and there's no reason why a professional adventurer would consent to bring one along unless it can demonstrate its competence.