I'd argue that inequality is the inevitable outcome if we are considering pure capitalism. The phrase "what we are currently allowing" only has meaning when there is an opposing force present to allow or forbid certain actions.

So it is certainly not an inevitable outcome if we are considering capitalist democracy. The level of inequality in a capitalist democracy is dependent in large part on the government. Most current governments allow huge inequality.

I'd also add that whilst the people in charge (whether running a company or a government) acting mostly out of self-interest is a problem, we also need to consider that self-interest can be charted with a time axis, and short-termist thinking is a huge and pervasive issue. CEOs will act to increase the share price right now, even if it's at the expense of what happens in 5 years' time, when it could well be someone else running the company. And governments are just as bad, if not worse. The Covid lockdowns in my view were implemented far too late, which exacerbated the economic damage that governments were trying to avoid in the first place by keeping society running as normal. Similar with the "too little, too late" response to the climate crisis.