Because champions are designed and balanced around their specific kit.
You gave an example of Darius with a Bltiz pull. That sort of makes sense because Darius already has a pull, so you're basically extending the range of his existing ability.
However there are several abilities in the game that would not make any sense on different champions.
For example, .. giving Ezreal Garen's spin makes absolutely zero sense. It would be funny to see, but it would just cause confusion.
Then there are champions who have abilities that depend on their other abilities. For example, if anyone was to get any of Azir's Q or E, they would need to have his W, and if they have his W they would need at least one of the other two.
The only way to be sure that this happens is to simply swap out the champion model but keep the whole kit together. Which again, would be entertaining but confusing.
Literally the whole game would be, "guess what abilities my enemy has" and that would be frustrating and incredibly difficult to play.