I think that is not much of a problem. You have to look at it in an over-generational manner:

Even the richest person dies. Maybe that person has inheritors, but if that's more than one person, that wealth is halved. Then you have to consider, that even if the likelihood is just 10% for one generation losing the family fortune, then after 7 generation the average likelihood is 100%. Just think about which is the oldest billionaire family and since when they exist? Is it the Rothschilds? The Al Sauds? Maybe something Subcontinental? The Rothschilds are now in the 5th generation and the Al Sauds in their 3rd. There was a descendant of the Moguls who's a trillionaire. But he got screwed over during in 2007 during the financial crisis (there was even a debate about it in the upper house because it was about a transaction that went over London). Bottom line: All wealth will go away. Just ask the Romanovs or the Quing dynasty. All gone. Bottom line: Old money is not really old and most families lose it after 2 generations. So, it's not really a persistence issue. Most of the billionaires worked for their fortune and then it's usually fair (criminal activity excepted)

Then there is the bottom end. That's also an over-generational issue. Growing into middle-class is an effort that takes 2-3 generations to last. But when a lower class family has more children than they can

• feed
• clothe
• house
• keep healthy
• educate
• (love!)

then you don't have to wonder about poverty. Especially Africa and the Subcontinent have lower classes which have an average of 5 children. What they should have is 1-2 children as an average. Just recently, Pakistans new census shows, the country's population DOUBLED within just one generation!

How the hell should it be possible to become wealthy at the same time? You need more infrastructure, more teachers, more land, more water, more productivity for agriculture, more jobs, more everything! That's doomed to fail, especially when the situation wasn't good before that.

The only country that did it the right way is China, which introduced a family policy in the mid 70. That was impart cruel and could've been done better, but it worked. Back then China had more people than India and was as poor and underdeveloped. Today, China is about to compete with the West and has an average income 5 times as high as India, which in turn is about to overtake China as most populated country on earth. Under such conditions, that is not a compliment.

Bottom line: You can get rid of poverty after 20 years, if you make sure, the bottom third of the population has an average of 1 child per family, while the middle third has 2 and the top third has 3 children.

Otherwise:

• When the upper-class has over-proportionally many children, then the next generation has a lot of genius
• When the middle-class has over-proportionally many children, then the next generation has a lot of stability
• When the lower-class has over-proportionally many children, then the next generation has a big problem.

Look at todays Africa, Pakistan and other places of that kind, you will see a lot of the latter.

My opinion therefore: The problem of poverty is not caused by rich people, but by unaccounted and self-inflicted long-term problems by the poor themselves (well, and their politicians..)

PS: Singapore did it that way and look at the place today..