No, the United States does not have a moral obligation to promote just governance in developing nations, because the United States does not owe things to other countries, simply because the United States is successful. The United States is often criticized for imposing its will on other nations, but then it is criticized for not helping enough. This is a no-win situation.
The United States should stop interfering with the perceived development, or lack thereof in other countries. Using any means other than verbal diplomacy to promote just governance is unacceptable. The US ought to demonstrate just governance at home where it's needed most and quit bulling the rest of the world.