If the problem is lobbying and corporate corruption of the government, I don't see how getting rid of the proxy and putting directly the corporations in charge will make anything better. Regulations may be imperfect and biased by lobbying, but having the corporations directly in charge seems even worse to me.

I agree that putting the corporations in charge of government would be bad. That's why libertarians oppose crony capitalism.

This is a kind of defeatist arguments. Here at Less Wrong, we speak of defeating death itself, conquering the stars, breaking the FAI problem, getting to the "level above" in understanding of the world, and yet, on this specific issue of politics/economics, we concede defeat so easily ? There are countless ways to "actually control the market" that we could imagine. Shouldn't we try to find a political system that ensures the market is controlled in a reasonably efficient way, rather than giving up ? Doesn't sound harder than solving the FAI problem.

Eliezer would probably argue that it's more-or-less equivalent to the FAI problem. Personally, depending on what one means by FAI I think it may well be harder. Specifically it may well be possible to create at FAI capable of managing an economy composed of humans, said FAI would not be capable of managing an economy composed of AIs of comparable complexity to itself, more or less due to the pigeon-hole principal.