No Morality

Morality represents how we want the world to work
Economics represents how it actually does.
-loose quote of the authors.

I think the focus on corruption/crime etc is simply because that is where the numbers are going to be inconsistent. Levitt looks at the numbers to find inconsistencies and then furthers those inconsistencies to draw a conclusion.
You would not be able to draw an interesting analysis from student's test scores (except if you are very invested in their scores), unless there was an inconsistency, in this case one that indicated cheating.

Baby names...I mean, the original pattern/trends of name selection is interesting, but what makes it more interesting is the indication of who chooses what sort of name when (the socio-economic implications of a baby's name).

I don't think that these sub themes are due to a moral preoccupation on the behalf of either author (“Freakonomics-style thinking simply doesn’t traffic in morality.” (p. 206)), it's just that within corruption is where the fascinating number are. Levitt and Dubner probably decided that to keep with the whole 'proving interesting things' theme, Levitt would have to analyze things that people find interesting, ie crime, corruption on behalf of experts, baby names etc.