HYPOTHESIS:
The function of that feeling of agency, volition, and intentionality has nothing to do with actual free will, but rather it is an an encoding process for our memory to help us distinguish between which of our actions was based on intelligent cognition and which of our actions was not based on intelligent cognition.
Perhaps by encoding some actions as intentional, it helps build a model in our brain for heuristically smart decisions so we don't have to recalculate all the variables every single time. In memory it's something like a model of "in the past, when I was being intelligent, I would do decisions in this way" and therefore that is my identity - the type of person who makes those decisions. So in a crisis, you can go back to your memory of your identity and get a quick snapshot of a behavioral pattern. Obviously, decisions that lack cognitive complexity would not be useful for this purpose, so we would not need to encode free will on behaviors like breathing and walking.