What gets me about this expression is that there are people who really are "high and mighty", but in a good way. They really do have the power and the authority to issue orders and command respect from other people. The owner and CEO of my company doesn't have an arrogant bone in his body, but I still respect him as the man in charge.
This expression really only applies whenever a person is ACTING high and mighty, but doesn't really have the juice to back it up. My older brother was like that when we were growing up. Just because he was born first, he thought he could rule over the rest of us. He knew what the right thing to do was all the time, and mostly the "right thing" was whatever HE wanted. Now that we're all adults, the rest of us like to remind him of his former "high and mighty" attitude.