I don’t know why so many people are mocking your (the OP’s) expression of the question. It seems pretty obvious what’s being asked and it’s a valid question.
We aren’t really capable of comporting ourselves in our daily lives as if we were not in charge of ourselves, making our own decisions. The people who believe in free will (as I do) would say that’s because we bloody well are the ones making our own decisions, whereas the people who believe free will does not exist would probably say it’s a compelling illusion, one that, as deterministically bound creatures, we are unable to escape. (There are also some people who claim to be living their lives without any experience of themselves as creatures of free will, but I think there’s a communications breakdown there – that doesn’t even parse, that’s like someone asserting that they are not conscious).
Temporarily setting aside the “free will, real or illusory” debate, yes it does make sense to ask what, if anything, is gained from embracing the belief (or perspective, if you hate to use “belief” in this context) that free will does not exist.
• Does embracing that notion put the person who embraces it more accurately in possession of a valid concept of reality? Assuming (for the sake of argument) that free will is indeed illusory, yes – but yes with an asterisk. If the illusion can’t be set aside, and a person’s life is kind of at the center of their own reality, we’re staring at a Clintonesque “what does is mean?” question here, aren’t we?
• Does seeing the world in those terms make a specific individual a “better citizen” / “better person” in some fashion? Maybe. Here, in particular, I think it is important to completely ignore the question of whether free will does or does not actually exist and look at the impact of the belief itself. It is thought by some people that in considering the behaviors of other people, those folks who think no one possesses free will woud be less judgmental and more compassionate. You see this notion crop up at least tangentially in a lot of debates about free will. The flip side is the notion that people who believe in free will, when considering the behaviors of other people, would be more vindictive, due to being inclined to think everyone is responsible for their own behaviors and hence should be judged for them.
On the other side of this same argument, though, maybe not. So far we’ve only looked at the effects of the belief on how folks might evaluate the behaviors of other people. The OP is focusing our attention on how folks evaluate their own behaviors. It does seem intrinsically nihilistic. If we ourselves do not choose our own behaviors, if we are merely reflexive biological contraptions in a stimulus-response equation, then we can never put our finger on any cause worth fighting for: there is only an internalized patterned response taking the form of a belief that some cause is worth fighting for, and now that the illusion of free will has been exposed, we realize we’ve just been programmed to see it that way. (so why bother; if we’d been born under Adolf Hitler’s exact situation we’d be holding his views, and worse yet there is no possibility of doing an evaluation that can say his views themselves are less good than the ones we hold now. NOTHING MATTERS) Keep in mind that we aren’t studying what it means for no free will to exist but what it means for individual people to believe that no free will exists.
• Does getting ALL (or most of) the individuals to see the world in those terms make the collective SOCIETY a better society, one that is more peaceful or less authoritarian or less chaotic? I dont think so. I think the proliferation of this belief, insofar as it is an individual-level disincentive to seeking social change for the reasons listed above, discourages social progress and creates a milieu in which it is difficult to argue that anything whatsoever is better than anything else whatsoever. It’s an anti-idealistic attitude, ultimately, in my opinion, although well-wrapped in the notion that it reduces judgmental attitudes.