If the question is should native areas be established in areas where they are in play adjacent to fairways, then in my opinion the answer is "no".
If the push to do so comes as an answer to tree removal, then it is no, because it defeats some of the reasons for removal; playability improvements and cost reduction, and the argument against, making the course easier, doesnt hold water, as described above. In fact, I would think native areas would have a similar negative effect on playability when compared to trees.
If the push to do so comes from taking maintained areas and letting them "go native", I imagine that the impetus would be to reduce costs, as you outlined. In my opinion, the answer would still be "no", or a "careful what you wish for" if the cost savings are compelling. Potentially reduced ability to hit recovery shots is the first unintended consequence that jumps to mind. (The type of area I am envisioning with these comments is an area that is predominantly native grasses, of the type that swallows wayward shots)