Exactly. It would've been a lot more comfortable and easy in some ways if we hadn't been shown things that could elicit sympathy for the Nobodies; but they gave us a six-hour prologue that made us love Roxas and Naminé and Axel, and presented the Organization as a giant grey area. Roxas and Naminé even talk about this:

Roxas: Organization XIII. They're a bad group!
Naminé: Bad, or good, I don't know. They are a group of incomplete people who wish to be whole.

Why was that theme even introduced, if we weren't meant to think about it?

I just think they didn't go quite far enough.

And yeah, exactly. That's why I say they're stunted, rather than completely emotionless. They feel just enough to know how empty they are. Even Saix, much though I'd like to think he just has no emotions, his dying action is a lament over his lack of heart.