That's not the White. That's Masakado, who is pretty much humanity's biggest champion.Hands-off is rather the point, actually. Being able to make a decision for yourself is important and core to what SMT is talking about, I'm absolutely with you there. But at the risk of sounding like a bad Philosophy professor, why leave it back up to humans? Law and Chaos are worse options for humans, but if we're doomed to go on repeat, then any suggestion of agency and self-determinism is farcical. Humanity therefore has no agency because it traps itself in its' own cycle. That's the first conclusion that the forces of Law and Chaos come to before proceeding to their respective solutions to that. Neutral is a rejection of that mechanically and thematically, and I don't think the message is 'we'd rather do this again if it means not getting YHVH or Lucifer in our shit' but 'we can collectively move beyond this'.
Regardless of how it turns out game after game, it's a persistent hope that drags along the Neutral end. That humans are worth saving and that you're doing something rather than actively working toward nothing.
And I wouldn't really take that quote at face value. Because, uh, the White aren't exactly people you're supposed to agree with.
But no, Neutral's theme is that what matters is that it's humanity's choice, humanity's decision when and how they end. That they're not going to give up their agency to a higher power because they promise a solution to the cycle. If they die, it's on their own terms. If they succeed, it'll be with their own two arms. That's what Neutral sees as worth fighting for! To reject the meddling of outsiders. It's why the protagonist cedes their power in the end.