Ah, yes, the Romney episode!
My first impression was Trump wanted to show he can rise above personal animosities and look to appoint the best people for the job, even if politically unfriendly. I also expected he would appoint some Democrats as well.
My second thought, however, before the final outcome was known, is that he was trying to humiliate Romney, by raising his hopes, then dashing them, all publicly. After all, as I said before, Trump is a naughty playboy billionaire, who can do what we mere mortals only wish we could, e.g., exact a sweet revenge on those who slighted us. All Romney had to say is "I appreciate the offer, but I don't see how I can reconcile working for the same man after what I said about him." Instead, he fell for the prank.