Inequality is not a challenge faced by a contemporary capitalistic system but a challenge brought about by our interventionist capitalistic model.
The question argues that contemporary capitalism faces the challenge of growing inequality, as if the wealthiest entrepreneurs have protected there interests under a capitalistic system. However, a capitalistic system requires market participants to follow the lead of that same market. How can wealthy entrepreneurs protect their own interests whilst also satisfying the needs of the market they must follow?
The alternative to a capitalistic system is an interventionist system, whereby a large body within the economy attempts to intervene with the natural course of an economy and control outcomes, such as growing inequality. Sound familiar? Interventionist systems only result in wealthy entrepreneurs not being required to solely satisfy the needs of the market, as they are now focused on building good relations with these controlling political factions to ensure these interventions are favorable. This results in corruption and inequality, making it harder to reduce the inequality gap within a market and economy.
For example, the high costs that result from market intervention by Governments make it harder for those less wealthy entrepreneurs to enter a market and compete with the large scale corporations who have the economies of scale to deal with these costs. Thankfully, technology has reduced the costs for those less wealthy to undertake new start-ups and compete with well-established market participants, therefore increasing the opportunities for entrepreneurs to build wealth. Opportunities to build wealth and compete with those wealthier market participants, through reduced costs resulting from technology, reduce inequality.