You are conflating an economic model with a political one. In fact, the central planner doesn't even need to be a person, but a set of assumptions and strategies that can be measured against the benefit they provide and be continually adjusted.
You touch an important point, however. The people most affected by Walmart's central planning, their employees, have no say in what strategies and assumptions the central planner uses and that removes any incentive to provide benefit to them.
The notion that these huge corporate bureaucracies are somehow "efficient" at anything except trashing the environment and homogenising and controlling - if not ultimately economically cannibalising - their own workers and customer base is clearly counterfactual.
From reading the book synopsis (again, I haven't read the book itself), it seems the authors are proposing some kind of democratic socialism rather than USSR-style authoritarianism. Is it workable? I have no idea. To me it seems that USSR-style authoritarianism and current Western neoliberal capitalism are but two small dots on the political economy spectrum. There are other ways of organizing society as well; certainly worth thought experiments to see what kind of other options there might be and what we might learn from them.
If all Walmart does is make mistakes then they go out of business. Central planning won't work but federated planning with 20 super corporations that are in competition with each other might actually be good enough. The only problem is that we both need and want the underdogs(startups) and this would undermine them.