For theistic evolution to be truly theistic it would also be unexplainable by scientific principles as you've defined them. If God had nothing whatsoever to do with how we got here (i.e., how human beings came to exist) then there's nothing theistic about our existence at all. On the other hand, if God did have something to do with it, then whatever method He used is intelligent design. If he created us outright, it's design. If he started the first microscopic life form and then guided it as it evolved into higher forms, it's design. If he started it and programmed it to evolve into us, it's design. If He had anything at all to do with how we got here, then it's design.
That's the crux of the debate here. It's why this debate will never be brought to a close (by humans, at any rate).
The idea that there can be some sort of "compromise" position is just word games. Telling Christians that they should support Theistic Evolution instead of ID or creation is silly. In order for evolution to be theistic, it would have to be design, and for that matter, creation. Likewise, if God had nothing to do with evolution, then it isn't theistic.
That's not the way "Intelligent Design" is defined.
"Intelligent Design" hypothesizes that scientists can prove that God created life on earth because there are structures which are "irreduceably complex" and thus, could not possibly have evolved through natural selection.
No. That's not correct. "Intelligent design" explicitly bases it's key inferences on the (purported) insufficiency of "natural causes" to explain this or that phenomena. Therefore divine employment of natural cause is not "intelligent design".
Since the Bible presents God as governing all of nature, including it's mundane and regular aspects, it is certainly theistic, yet excluded from ID, to argue and understand that what God accomplishes through natural phenomena is part and parcel of His manifestation as Creator.
I would argue that ID isn't even theistic, but rather deistic. It wants to make God (in the guise of the "intelligent designer") the author of this or that aspect of creation. Theism (IMHO) must hold that God is author of all creation.