Capitalism is explicitly designed for private (top-down) ownership over the means of production and the subordination of labor to capital. The fact that there is ungodly wealth inequality, to the level where a mere seventy people control more wealth than half the world, is not “a flaw in the system”. As long as autocrats make all the major economic decisions, you’re going to wind up with a system with less equality and less freedom by default.
And yes, that applies to both “corporatism” and “true capitalism” – either way you slice it you still have economic authority and ownership concentrated in the hands of a minority class of elites. This minority class controls the workplaces we labor in and the housing we live in, and they reap the rewards produced by us because of their ownership. Capitalism may be a different economic mode from feudalism, but you still fundamentally have a majority class of laborers generating all the goods that keeps society functioning while a parasitic ruling class accrues the bulk of the utilities. These are class relationships; “power-over” relationships.
They fuel hierarchy in other areas of life – sexism, racism, ableism, homophobia, transphobia, xenophobia, and imperialism. Social problems are overwhelmingly traceable back to the roots of social organization: the economic system. The elite owning class would prefer a divided population so that common interests aren’t recognized, and so the system benefits some people proportionately more than others. This is where privilege comes in – and yet, the conversation is incomplete if one leaves out the material basis for which patriarchy, white supremacy, ableism, and cisheteronormativity operate. We can’t expect hierarchical bigotry to dissolve as long as we have a class-based economic system.
Economic democracy is the way forward. A new system focused on meeting human needs through direct democracy rather than on accruing profits for capitalists through concentrated decision-making. If capitalism creates huge wealth chasms AND deprives people of the ability to influence decisions that affect them, then socialism should aim to do the opposite – genuine social equality (a lack of “power-over” relationships and equality of access to social utilities) achieved through democratic organizational structures (horizontal workplaces, communal housing, common land returned to the commons) where individuals actually get to have a voice in the decisions that affect them.