But the reason that when talking about the 1% they suddenly stop looking globally and only look within countries is that everyone in the UK and US is top-1% worldwide. Equalizing would make the average wage $500, or 375 pounds. And when you start discussing what countries are the problem ... immediately you see there are very few poor democracies. There are some, but not much.
To make matters worse, this year's Nobel prize in Economics went to research showing that the problem is governments, and specifically that a lot of populous countries don't create institutions to improve the welfare of people at all, but rather focused on stealing from the population. This makes it an unfixable problem in those countries. More than that, a lot of these countries' populations don't want to fix it, or even want to make it far worse (like Egypt, or Iran, or Pakistan, or Sudan) for a whole host of reasons.
Oh and most of those governments are "captured by wealth" only in the sense that the current rulers exploit the population for their personal wealth. This is what you see from Afghanistan to Venezuela, but those governments didn't come to power with wealth. Various ideologies brought these governments to power, and the governments steal the wealth of the people, even to an extent that people start dying in pretty large numbers like in Afghanistan. I also find it strange that when discussing capture by wealth no-one ever takes Venezuela as an example, despite how obvious it is that that's the problem there. Nobody discusses how Chavez came to power as a "communist" and died a billionaire.
So if you want to fix poverty, one of the things it looks like you'll have to do is to overthrow the governments ruling, actually more than half of humanity, and convince their populations to stop caring more about religion and other ideologies, like pride, or a mostly imagined enemy (like Pakistan), than about prosperity.