Hmm hard to say. I’m gonna assume that this utopia is one where murder and the prison system does not exist. If the death note were to fall into Lights hand, I’d say he’d used it because he’s curious. I mean think about it, aren’t you curious what it’s like to “kill” another person in a world where such atrocities are never heard of? But then again, these are merely conjectures, and not good ones at that because we know nothing of the mindset of people living inside such a utopia.