Surely because that's history, we don't teach it that way because then you lose the links that have [much] later been found with other areas of maths -- isn't it the linking in to different areas that provides all the power? We want current students to understand a far wider curriculum and realise the links that come out of those abstraction, no?

I guess it's like whether you teach grammar to language students or hope that through language use they'll derive their own abstractions that allow them to understand the grammar sufficient to say things that they've never heard before.

From a history perspective we probably don't know how they came up with the idea, even if their journals (!) had a specific derivation of a proof then that wouldn't mean that was their initial direction of travel necessarily.