... the Pythagorean Theorem depends on the assumptions of Euclidean geometry and doesn't work on spheres or globes...
If a "proof" of the Pythagorean Theorem does not bring in the Euclidean nature of the space under consideration, in what sense can it be considered a proof at all?
According to this wikipedia article, the "Euclidean metric" -- which could also be called the "Pythagorean metric" -- is actually one of the axioms of a properly-specified Euclidean geometry.
More interesting (to me, at least) would be a discussion of how the Pythagorean Metric leads to our concept of geometric area.
Sorry, I just can't see how doing it the other way around makes sense.