Inheritance isn't the problem, property is the problem. As technology (the means of appropriation) expands, alongside the scope of association (size of firms, national populations), so does the ability of a group to generate a huge amount of wealth. When that group's productivity is allowed to concentrate in the hands of few or one because of some arbitrary claim to authority over the group, like property-- or divine right, or whatever other excuses autocrats have used throughout history-- the acceleration of production through improving technology and expanding associations will always yield wider inequality.
And property can exist only through violence, so we find ourselves always at square one-- a coercive and autocratic society-- in property-based social orders.
I would add that at least in the past 10k-20k years a higher level of Techs made your group/tribe/people also more competitive towards groups/tribes/peoples, in effect eliminating them by war and taking over their properties.
Which makes the MAD geopolitical situation a new era where classic war diminishes in importance, the UN there as well.
Another basic factor driving inequality, the population growth in many underdeveloped countries, has almost come to an end. There are only a few countries left that grow , and BTW grow much faster than their GDP, their food production, etc, etc. Kind of stupid those countries do not get more attention from the UN and some rich countries to tackle that (the population growth). By now our understanding of socio-psychological factors is good enough to help out.
Property is ofc still there and in the possession of the powerful.
But also there the end of the two main pillars of that is coming within sight. The pillars Knowledge and Techs are still heading steady for a post scarcity level.
As of today, in my country, if the current prosperity level would be considered as "good enough", we only need to work 50% of our life. After further AI this could be down to less than 25% in 2100.
Meaning also that we, the people, can decide to get rid of further fast track growth of the economy, can get rid of the oligarchical powers, and develop slower, with some technical ineffeciencies, but on our own terms.
The real issue I see there is that the oligarchical powers will not like that (for me inevitable) development, and will get access or even possession to domestic violence, control the police, through influence on the "democratic" politicians,
or more likely and more worse.... buy or manufacture themselves AI Robot units to keep "us" under control.
Perhaps all in all just another 50-100 years to go before we get into that situation
EDIT
one of the nice things about the strong hierchical character of (oliogarchical) companies, is that you only need to chop off the head, to get control over the whole body, that does useful things.
Same advantage you can see all over history, that when you defeat the army of an dictator, with an oiled administration below him to rule, you normally gain control over everything.
Alexander the Great and Persia as nice example.