The demographic crisis is just starting. China and Europe are both going to be hit hard in the coming decades because of the replacement rates and aging populations. If anything, mass immigration might be Europe's only option.
Completely eliminating privilege is not the same thing as everybody having the same thing. It's the same thing as everyone playing on a fair field where all costs and decisions are internalized by those who make them and not put onto others without their consent. Human nature is a spook, and doesn't actually exist. There is no universal "nature" which can be ascribed to the 7 billion persons on this planet. Each individual has different wants, interests, goals, abilities, and disabilities. When we speak of "human nature" we gloss over that.
There is no leveled play field since people have different capabilities... and although everyone likes to paint human as the most evil creatures on the world, you won't find species that take good care of the elderly to the point human does, won't find the level of empathy for the disabled, etc.
Leveled playing field =|= equality in outcome, so I don't know why you're speaking about capabilities.