Private ownership isn't anti-monopoly, though. Big fuck-off monopolies are the best way to deliver rents to shareholders, which is capitalism's objective function, so ownership and management pursue the goal with a single mind and eventually they succeed. Eventually they find a combination of vertical/horizontal integration, economies of scale, network effects, platform effects, last mile dynamics, regulatory capture, and ownership rights that lock out competition. It's all they talk about, it's all they think about, and if you try to deliver a pitch to an investor without some kind of plan to build an anticompetitive moat god help you, lol.
I'll believe that capitalists believe in competition when they start passing policy that promotes it. Policy that tax disadvantages large corporations to encourage them to break up. Policy that winds down the "cheat codes" that business students and boardrooms salivate over. Policy that prevents political influence from becoming just another route to investment return. Policy that makes it easier to do incorporation/payroll/taxes/benefits for small businesses. Until these things happen, I see capitalism as just one more flavor of the same old empire-building dynamics that stretch back through time.
And not necessarily the winning one. Selling the industrial base of the United States economy to the Communist Party of China in order to pump the assets of wealthy Americans was a real six dimensional chess move. I suppose we'll see how it turns out.