I think the entire world would be changed for the better if people practiced the "Do unto others only as you would have them do unto you" rule. We have become rude and self centered, lacking in common courtesy. We cut people off in traffic, we don't give up our bus seat for an elderly woman anymore, and we scream at people in public if they forgot the ketchup on our cheeseburger.
I do believe the "do unto others" lifestyle has potential to change the world if it were to be followed by the vast majority of people. If this practice was followed to its truest form, I believe it would help "open the eyes" of people who practice hypocrisy and hate toward others.
I truly believe that if everybody on the planet followed the Golden Rule, it would change the world for the better. Unfortunately that will never happen. Morality and ethics is something that is varied with some people. And some people just don't care about it. That's why such a scenario will never occur.
There are many things people want done to them that others would not want done to them. In short, it is a decent heuristic but cannot be a good basis for public policy or even private action. Ethics cannot be reduced to simple rules or phrases as situations frequently arise that challenge even elaborate systems of justice.
No, there's no reason to believe people would follow the Golden Rule as it goes against hundreds of thousands of years of history and human nature. If more people followed it, it would just mean that more people would be taken advantage of, which wouldn't really benefit humanity as a whole.