I really don’t think this is true in a meaningful way. Despite your appeal to cannibalism (of all things), it certainly is natural for people to want to help their family and friends. Without that instinct, we have neither.
Whatever the solution to inequality, it will need to take into account that people like helping people they like. This is why social programs like free healthcare and education are so important - we need to neutralise the benefit of “tilting the scales”, rather than asking people to change perfectly reasonable behaviour.
My point is that the desire to “tilt the scales for their kids and their social class” seems innate, and any mechanism that we create to improve equality needs to take this into account at a fundamental level, or it will either be rejected or compromised.
But this only works if there is true equality of opportunity with completely open universal access to education, health, basic tech and tools, high quality unbiased news, and social opportunities.
The real cause of inequality is privileged parents trying to tilt the scales for their kids and their social class.
You may say "That's only natural" - but so was cannibalism until we worked out that it's a really stupid idea and does a lot more harm than good.
The real costs of unearned "elite" family privilege are almost unimaginable. We're so used to how things are that we can't even see how much this arrangement has blocked progress in every discipline.
Not only does it pollute politics, democracy, and the media, hoard resources uselessly, and cause untold human suffering, it also guarantees that most of the talent in each generation is suppressed and wasted.