That is more than a theory it has been done in the real world. A Tibetan king, distressed by the disparity between the poor and the rich, ordered that all wealth and property be divided equally amongst the population. It was and one year later those who had been wealthy were wealthy again and those who had been poor were poor again. The king ordered that it be done again. One year later the same result. The king ordered it done a third time and again within a year the rich were rich and the poor were poor again.
He was one of the early Buddhist kings who did this because he wanted to end the suffering of the poor. He learned that people have their own karma which they have to work out for themselves it can't be "fixed" for them. That is the purpose of retelling the story to Buddhist students today.
Whether you believe in karma or not it was proved three times over that it's not possible to end poverty by giving the poor wealth taken from the wealthy.
Over a longer time period, it would be observed that some of the rich eventually became poor, as a consequence of either poor decision-making or accidental circumstances (illness, natural disaster). In the same period, some of the formerly poor would become rich, because of good decision-making or good fortune.