The Sneak Attack class feature is carefully worded to allow this possibility, and your conclusion is that it is "poorly designed"? Oookay then.
It is worded such that it is technically possible, but there's no way to know whether that was actually intended or simply an oversight unless we consult the designer in charge of that section. Given the degree to which the game rules were in flux even
after the PHB came out (note discrepancies between monsters in the MM and monster guidelines in the DMG), it's entirely possible that the designer
didn't know that it was possible to use Strength with a finesse weapon when they were writing it (or when it was being edited afterward).
And yet Conan of Cimmeria is both the iconic barbarian and an iconic rogue. You may need to broaden your ideas about what these classes are "exclusively" designed for.
I've read a couple of Conan stories. Conan the Barbarian is the iconic barbarian. He rips people apart with his mighty thews, and he sneaks up on people because he's a Mary Sue with ridiculous stats. You
might be able to argue that he's a fighter or multi-class fighter-rogue, because he doesn't really rage and he has a lot of skills. However, he definitely
doesn't rely on backstabbing as anything more than a one-off circumstantial event - sneak attacking isn't the fighting style that they describe him using - and his distrust of magic was also a strong influence on the barbarian's magic-hating former incarnations.
The iconic rogue is the Gray Mouser, who dual wields and can read scrolls, and Conan is extremely
not that. D&D is a class-based system which works on the premise of strongly-codified archetypes. It is not a game of subtle nuance.