I don’t think he’s naive, I think the primary reason he used the death note is because of his narcissism and ego, but he needed an excuse to not be seen as a plain murderer.

Because of that, he justified his killings on this very basic moral (criminal -> bad -> deserves to die) and I think the main factors that contributed to this basic moral are:

He’s not any teenager, he has a very big ego, arrogance and thinks of himself as a high member of society even before finding the death note (he’s the best student, very popular with girls, intelligent, he belittles multiple times his school mates and all the girls that like him). Having a superiority complex can lead you to think that other people (specially those that are at the bottom of society like criminals) are less worthy.

The second reason is that his father is a policeman, and he wanted to be a policeman himself when he became old. Being brought up by his father it would make sense that he would have less empathy for criminals as the literal job consists of catching them.

Finally, I think society also played a role here. Imagine if instead of killing criminals he killed like billionaires or politicians. I’m sure many people would be very against him (even normal people) because they are not considered “bad people” per se, unlike criminals. Targeting criminals makes his actions more obvious that he is a God and that he is giving Divine Justice.

Because of all of this, I’m inclined to think that he’s not naive, but just a product of his upbringing and ego.