Looking at psychology, in general we see people who feel like they have agency in their lives are happier, and people feeling like they have no agency are depressed. Our agency allows us to do great things, like spearhead interesting projects or just make our lives better with our choices.
Some people will link free will to the conscious experience, but I don't think that's quite right. We all know that we are 'aware'. But being aware, experiencing life consciously, doesn't make a difference to whether we are watching some great cosmic play being preformed.
In fact, the way things happen in life, all things being the made up of cumulative events from the past, it be strange if things weren't predetermined. To me personally, a bit of hypocritical belief is necessary to continue acting out the play.
If nobody can conclusively say anything about "free will" - if all we can agree on is that it's intrinsically ineffable - then it all starts to sound a bit like Russell's Teapot, or angels dancing on pinheads, and we should probably focus our energies on something more effable.
However, free will in the sense of a soul commanding a body separate from that body that is tallying up sins to be punished based on those decisions is hard to believe.
But to falsify a concept like "Free Will" it needs to first be defined. It's one of those things where you can get 1000 different definitions.
The problem is, this view really doesn't match with our experience of what it means to live as human beings. We experience deciding. We become convinced that things are actually true. We love and are loved. We know, from direct experience of living as human beings, that this is not who we are.
This leaves a dilemma. Either our experience is wrong, or our initial starting point is wrong. Either the laws of physics are not what is "furthest back" (in Francis Schaeffer's term), or else we really are determined and our lived experience is an illusion.
Choice is deterministic, but that doesn't make it less real - on the contrary, it gives your choices meaning! They have causes, reasons, justifications! It would hardly be preferable if your "choice" were the outcome of a fair dice roll, would it? What kind of choice would that be?
I think the problem arises from a confusion of of abstraction levels. At the level of atoms and chemical reactions, you are completely deterministic and "choice" isn't a meaningful concept. 10 stories up, at the level of thoughts and ideas, it is. This is no different than how "pressure" is a meaningful concept for a tank of air, but not a single air molecule.
If your view is that Brownian Motion is not deterministic then does that not contradict the idea 'that cause and effect holds in a closed system' as any sort of absolute?