The quibble I have about "Divine input" is that in order for it to be seen as a valid part of how nature behaves and scientific, there must be some understanding of how and where it happened. Eventually, it has to be measureable.
It is insufficient to wave hands and say God did it. One must be able to say, "ah it happened here at this time, and all the evidence points to it."
The burden for the creationists/IDists is that "God did it" can be used by the uneducated any time they like to "explain" anything they don't understand. Since GDI explains everything, it explains nothing.
As I said, I'm willing to entertain the idea that a Divinity had some input into evolution. However, at this time it is not measureable. What is clear is that the evidence from geology precludes the theory of a 6-day creation and a global flood etc. This means that the Bible is simply a book of allegories and stories.