Actually, not every Uchiha is born with the innate affinity to use fire. They train in it as a right of passage regardless of the affinity they're born with. Sasuke was born with lightning affinity, but trained to gain fire proficiency. Itachi was likely born with fire, and trained to gain water later. Unless you're born with a KG that grants you a compound element by combining two elements, you're likely not gonna be born with an affinity for more than one element.
EDIT: That said, it makes sense that Uchiha would branch off into multiple releases, as they would get the most use out of their "copying eye". Remember, they can't copy a jutsu unless they:
1: See the handseals
2: Have the necessary chakra to make it work
3: Have the necessary elemental affinity to make it work
Sasuke would never be able to copy Doryuu Taiga (earth jutsu) even if he had enough chakra and saw the handseals because he doesn't have the earth elemental proficiency.
Another reason for them gaining other elements is, quite simply, it's stated that most Jounin level ninja know atleast 2 elemental releases. If the Uchiha are indeed elite, then they've reached/surpassed Jounin level, right? So they've likely passed the prerequisites to be considered Jounin aswell.
