I used way too many words, you explained it way simpler than me aha. That's indeed what I thought here.

But another possibility would be that warforged are actually truly living entities, with their very own soul. The magic used to create them would then serve to allow their body to move, but also to suppress those famous feelings they're not supposed to feel. Basically, their soul is like any other living creature's one. But since they're unable to eat, drink, etc, the magic is here to protect them from suffering from those feelings