The important aspect is competition. If you have multiple central planners that compete with each other then maybe it could work out as well.
So, similar to how capitalism does it?
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.
A newfangled med school could conceivably lecture on "Smoking, causation and the cancer of old age" in the intro course, and still turn out great doctors.
But it should raise some questions about who backs the school.
But much more concerning is "1.9 Capitalism, causation and history’s hockey stick".
It starts off questioning whether capitalism actually did cause the great hockey stick. It then presents the German case study pretty fairly but then ends: "We cannot conclude from the German natural experiment that capitalism always promotes rapid economic growth while central planning is a recipe for relative stagnation."
While it's true that one case study isn't conclusive (and the absolute term "always" was used to weaken the hypothesis), the closing paragraph leaves the reader with the impression that we only have one data point so we're not that sure which approach works better.
Edit: On the other hand, it is honest about price controls. And it does actually incorporate supply and demand curves in later sections where appropriate.