Wait, we already have such central planning boards - Uber, Fedex, Walmart, etc. My mistake.
You are correct that things like advertising are (sometimes) zero sum - specifically, advertising based on irrational criteria. (Advertising which transmits useful information, e.g. "taxis suck and Uber exists", is not zero sum.)
But you also gloss over one of the big benefits of a non-centralized system - correctly finding the utility function. In a centrally planned system, your utility function needs to properly identify what tradeoffs people would make if they had the choice. This is not easy, and modern computing doesn't help very much here.
In contrast, consumer choice via price systems handles this nicely.
this is of course valid for humans, who have all kinds of flaws, some more than others. so you propose to give power to software, who by principle always has... flaws. imagine how juicy this thing would be for hackers, who would have billions-big incentives from shady business people to nudge decisions in their favors... silly naive people :)
What I would suggest - let some state of the art simulation run along the humans, and evaluate its decisions after some time passes, to clearly see who made the right one, in long term. after there is some long term perception that computer is clear winner (definitely not below 10-20 year mark of steady performance), we can move that way. and always, always have some sort of semi-neutral commitee to oversee and accept/reject all important stuff (with necessary reasoning, not on whims of current most powerful one). make it as transparent as possible. -- do you think this is real? no way, when looking at how shady today's politics are done, be it US, europe or any other place...
If you want proof of this, consider why work-to-rule[1] works. While it is obviously intended to be used as a type of strike or similar direct action, the idea is that you are technically doing you job too accurately. The work continues to function thanks to the fact that almost nobody does everything they are technically supposed to do. We speed on the way to work, we overlook minor mistakes, we fix instructions and reinterpret orders. Reports are regularly sent up the chain of command that "yes, project $FOO was finished on time" even though everybody involved knows it wasn't.
The idea that you can take known-bad data, apply it to a fantastically complex model, iterate that model to add unknown amounts of chaotic noise, and get usable results is completely insane. Given the realities of how bureaucracies work, that noise will simply be re-interpreted until it says whatever the people involved want it to say. In the end, it is still a situation where the people making decisions are distanced from the consequences of their decisions.
If you want to fix some of the problems we have, I suggest that we need a lot more of the opposite of central planning: local decision making authority. A control system tends to work better when it can get accurate and immediate feedback, and in human terms that means experiencing - or at least directly seeing - the consequences of any decision. We, as a species, are notoriously terrible at evaluating any decision where the consequences are not felt immediately and personally.
But even assuming that some people will abuse the system (as they do today and we still live with it), it seems plausible to me that the economy would still run better if everything was driven by global optimization algorithm fed with real-time data.