I'm not sure the example of the US is a particularly good endorsement of that strategy.
We have promoted democracy and human rights to varying degrees and have never applied those standards consistently. So you end up with it being a problem that people in Cuba who speak out against the government are put in jail, but for some reason it's not a problem when that happens to people in Saudi Arabia. And as a result, people in other countries largely don't take us seriously on those issues anyway.
Trying to promote democracy and human rights in Afghanistan and Iraq was done at the expense of trillions of dollars and thousands of American lives. It wasn't worth it. If Iraqis had really wanted to be rid of Saddam Hussein, they'd have gotten rid of him themselves. If Afghans really cared about their daughters being able to go to school, they'd have defended their rights to do so. India or Brazil would be crazy to embark on a misadventure of that scale.
This is the biggest point. I sincerly think the US should form a league of democracies but that is really hard when the US isn't consistent. We shouldn't be allies with Saudi Arabia. The US needs to be more even handed in the Israel-Palestinian conflict.
Of course, no one that can make up for the US invading Iraq.