I feel like in this comment you're putting your finger on a general principal of instrumental rationality that goes beyond the specific issue at hand, and indeed beyond the realm of mathematical proof. It might be worth a post on "engagement" at some point.

Specifically, I note similar phenomena in software development where sometimes what I start working on ends up being not at all related to the final product, but nonetheless sets me off on a chain of consequences that lead me to the final, useful product. And I too experience the annoyance of managers insisting that I lay out a clear path from beginning to end, when I don't yet know what the territory looks like or sometimes even what the destination is.

As Eisenhower said, "Plans are worthless, but planning is everything."