Oh my! There is a lot of counterfactual points to unpack here. This whole notion of inherited wealth is way less of a problem than many think. The majority of those with wealth did not inherit it, and in fact within 2 generations 90% of families will have consumed that wealth.
Capitalism and free markets are not perfect, nor are they fair, but in essence perfect fairness and equanimity are impossible targets. We are all born on different points across different axis. Some are more intelligent, some more attractive, others taller, some born into wealth.
What Capitalism and free markets do represent are more efficiency which in turn creates more opportunities for more people. However it’s pretty clear to see we aren’t living anywhere close to an efficient system, social mobility has stalled. Corruption is expanding, and the root of this is we live under a globalist crony capitalist system. Which is a rank perversion of free market principles.
This came about because we put our social safety net at the wrong end of society namely at the top end. With the idea of banks and institutions that were “too big to fail”. Rather than guarantee the savings of citizens who had their savings in a bank that that was about to fail, we bailed out the bank. Very bad move indeed. Furthermore fiat currency since we moved off the gold standard has meant with policies like quantitative easing, the rich (who gain access to the purchasing power of the billions created) gain the full purchasing power of that currency before it passes onto the likes of us once the value has been diluted.
Unfortunately communism/socialism are not the answer, not because they are bad systems they are actually rather good. The principle of each according to their need and the each according to their ability is a perfect principle for a family or small community. These systems however work atrociously at scale. As evidenced by each and every time they have been attempted at a nation scale.
The answer in my opinion (not that it will lead to a utopian ideal mind), is to follow this pattern: we figured out it was unwise for the government to also be the military as then we get warlords and conflict, we also hit upon separation of Church and state otherwise everyone fights to operate the levers of State power to favour their religion and repress others. The next great advance in human political theory will be the separation of state and economics, as this is the precise issue of wealth leveraging untoward influence over politics that produces the sort of crony capitalism as well as undermining democracy itself.
We are still a long way from figuring this out though, probably generations in fact, but the clues are there.