If you think that Bruenig is arguing for price controls without any qualifiers, you read the article wrong. He is arguing for equality, because equality is a necessary precondition if you actually want to get the full benefits of a price system (among other reasons). I have yet to see a convincing counterargument to that point.
You may have been misled by the part about the theory of the second best (which is a common point in economics): since the best solution (eliminating inequality) is off the table for political reasons, you have to turn to second-best solutions. Under certain circumstances, that can mean price controls.
But yes, the best solution is to eliminate (or at least reduce, as a first step) inequality. For example, taxing the rich and giving to the poor, as you point out yourself (which is where we're back at you agreeing with Bruenig ;-)).
And I never said (nor was given reason to think that) the best solution is to eliminate inequality, so I don't see how I'm agreeing with that. And I take that seriously because I mine every article for information that would force me to switch to a worldmodel with more explanatory power; this one (like most clumsy attempts to prove the pointlessness of prices) fails at that.
Taxing the rich for foodstamps is not eliminating inequality, and is not rightly regarded as a "first step" towards a policy that does; only a tiny fraction of foodstamp advocates want anything like the radical equality required for his model of this problem to apply.
The problem with argument's like Bruenig's is that they double as fully-general counterarguments against the entire concept of a price system, and in favor of strict price controls. You could make his exact points against e.g. allowing some foods to be priced more than others, with the same points about "the poor value the food more, it would go to a random population rather than just the rich", etc.
There is too much wrong with that argument to point to any one thing, but suffice to say, even the most pro-poor nations reject it.
That's why every sane nutrition policy is more like "tax people, give the poor money to buy food" rather than "all food [appropriately quantified and defined] should be cheap enough for the poor to subsist on, and if you want to sell any food at all, you must sell it at that rate".