Doesn't the existence of wealth inequality, as well as crimes committed by wealthy people, disprove the idea that humans are inherently altruistic?

When questioned as to what will motivate people to work in the absence of personal profit, most socialists/communists will say something along the lines of "the good of the community", "helping their fellow man", "contributing to humanity", or something along those lines. They'll also usually elaborate that if they had their basic needs met and enough leisure time to enjoy personal hobbies, then they would be happy to spend whatever time they had leftover on helping others, or that they would happily give away any surplus goods they had for free to anyone who needs them.

Essentially, they would voluntarily and without promise of profit (or any other external motivator, like reciprocal favors) give away surplus goods/labor to people in need. Thus, they assume innate altruism in human beings.

However, there are wealthy people right now who have all of their basic needs met and have plenty of time and resources to pursue personal hobbies, but don't give away their money or spend at least some of their time helping others. They seem perfectly content to ignore those in need and don't seem to feel any obligation to help their communities. Not only that, but many wealthy people actively choose to harm others via fraud, exploitation, money laundering, and even violent crime like rape, despite the fact that they are not poor or desperate and already have everything they need and more. This phenomenon isn't exclusive to uber-wealthy billionaires, either; crime exists across all income levels, with the only real difference being in the type of crime (wealthy people commit more white-collar crimes as opposed to poor people committing more street crimes).

I guess my question is, if people are inherently altruistic, then why does wealth inequality even exist in the first place? Wouldn't the wealthy just feel compelled by their innate altruism to give it all away to people in need? And why do people who already have everything they need to live comfortably choose to harm others for their own selfish gain, if all it takes for humans to act on their innate altruism is financial stability (which these people have)?

Also: to preempt the "they're all sociopaths" answer, the highest estimate for sociopathy among the wealthy seems to sit at 1 in 5, or 20%. That means that 80%, the vast majority of the wealthy, do not qualify as sociopaths. Not only that, but adolescents with antisocial tendencies are more likely to end up poor, not wealthy. And among the homeless population, there is a substantially elevated rate of paranoid personality disorder, antisocial personality disorder (the medical term for sociopathy), and borderline personality disorder, all of which are strongly linked to reduced empathy (here, here,%20is%20a%20%C2%B7,small%20percentage%20of%20individuals%20experience%20significant%20improvement) and here). So "the wealthy are just abnormal, the majority of humanity isn't like this" doesn't seem to be the answer to this question.