[stared]

To some extend it is countering Carl Friedrich Gauss' approach of "No self-respecting architect leaves the scaffolding in place after completing his building".

Yet, that way we abstract a proof - compare with a programming library that can be used "as it is" but there is not as much insight into details.

Oftentimes, such scaffolding is didactic - allows to us to learn why a given path was taken, why a "simpler" or "more straightforward" approach didn't work. I would be something like "negative results" in mathematics, no in terms we proved negative, but for some reasons a different approach does not work. Sometimes it is also good for grounding intuition of sorts.

Vide https://mathoverflow.net/questions/459252/when-has-the-scaff...