I agree that inequality will always exist, but I think that inequality growth has been institutionalised and we need to change that. The system is like a vacuum cleaner, sucking money from the poor and delivering it to those who control the machine. If you give more spending power to the poor, it'll get sucked up, too.
The things is that the vacuum cleaner doesn't belong to the few. It belongs to everyone. Make the people who control it pay rent to the rest of us if they want to use it and pretty soon they may see that it's pointless to use it.
I agree that the problem is systemic and that it is systemic because of human nature. The vacuum cleaner in effect belongs to those who control it - they have taken control of it. Humans are selfish by nature and those in control won't simply hand over control to those without the power to convince them to do so. An independent means needs to be applied to empower the powerless.