The problem I have with the idea of "managing the economy" is that we might not even know what that phrase actually means. I often read "economy" and translate that as "runaway complexity." I sense this complexity in a system of such magnitude, involving so many interacting systems, and so many individual actors (many of which are computer programs at this point, I think) that it simply cannot be grasped by any single human mind, no matter the training or intelligence. This is just my sense of this; am I wrong? Someone here, please educate me.
Do you know what your neighbours want? What they like and dislike, what they want for their children, and so on?
Now, do you think a genius would know? And if he knew, would he know better than them?
You can "run the economy" (that is, rule other people) to achieve your goals (e.g. if you are a pharaoh and want your own pyramid) but you just can't go against people's will to help them achieve their own goals.
I agree with you inasmuch as an economy is about people, but what if it isn't about people so much as some larger "thing" (an incomprehensible interaction of systems, perhaps?) that individuals, and even governments, have to deal/interact with? What if that's just as true for the so-called global "elites" as for the rest of us? I suspect that it is. I think that what you say about people controlling other people is accurate; I just think it's only a small percentage of the data we have to account for.
If it isn't about people, who or what could it possibly be about? What other data are you looking for? What do you think is moving the money around? The economy isn't some magical system that randomly shuffles dollar bills around, it's people and businesses buying things.
"Managing the economy" is not what Keynesianism is really about. It's about correcting a specific flaw in capitalist economies (the existence of multiple inefficient equilibrium positions). The idea is that once you correct that specific flaw, the economy will run itself better.
To look at it another way: Keynes argued that no one can manage the market, including the market itself. But that doesn't mean it can't be managed better than it is.