Capitalism isn't about markets. Capitalism is defined as private, not state, ownership of property. Nothing in capitalism's basic theory requires markets.

It's just that capitalism, sans monopolies, and markets are a natural fit for each other. Capitalism with monopolies is the late 1800s US, which was an economic disaster for many and why we saw a rise of unions and socialist groups at the time.

Sure. But if one central planner is better than two, because price controls would work better without competition, then it should stand to reason that even more than two planners would be even more effective. If the entire market were involved in price-setting, it should be optimal. Sure, there's probably a point of diminishing returns on how many people are needed to make price controls more efficient, but it seems likely that the point of diminishing returns isn't proximally close to 2.