Why can't we simulate an NP oracle with an NP machine?
You don't have exponential time, what you have is a nondeterministic polynomial time machine. 

What you can try to do, in order to simulate the oracle call to $\mathcal{O}\in NP$ on a string $s$, is to run the nondeterminstic polynomial machine $M_\mathcal{O}$ on input $s$. If $M_\mathcal{O}$ returned "yes" then you know $s\in\mathcal{O}$, but if it returned "no", then you cant be sure, and you don't have enough resources to try out all possible branches in an NP machine.