But surely we believe in "free will" not because we observe it in a lab but because we experience it directly. Pick up a menu at a restaurant. Sure there is mechanistic cause and effect going on in your selection—memories, sights, smells—but there is also the direct experience of choosing. Whatever free will is, it has to do with this experience of bringing a cause into the universe essential ex nihilo, from within yourself.
Science is always compelled to dismiss these individual and personal experiences and perceptions, and as science rightly so. But as people we can take them into account. And so we should. To dismiss the sense of "I" that makes us, in fact, people is to cast away perhaps the most important part of our world. We retain a sense of choice, of free will, not because it's a compelling illusion but because it is in fact in large part what we are and what we recognize others to be. Be careful with that word "illusion": you can call something an illusion, but you then have to account for where the illusion came from and why it functions so powerfully. I'd say that free will is not an illusion so much as a thing that science deals badly with and is therefore tempted to dismiss. Well, dismiss free will from the laboratory, sure, but don't pretend we aren't free-willing things or you'll be left with nothing but a lab, populated by not-quite-people.
Is this sort of what is meant with 'qualia'? I could never quite wrap my head around what that concept means, in what context, and what its value is.