It wasn't obvious to people living thousands of years ago that science would be the way to move civilisation forward, but here we are. And just because it "doesn't follow" that these methods would improve science when applied to itself, doesn't mean that the latter idea is false either.

We follow these principles out of observing history. But part of it is an act of faith, I'll give you that. What sort of "evidence" are you referring to, that it would be harmful?