This reminds me of the common academic economist's stance on the FDA. The idea is that the FDA is unnecessary, because food and pharmaceutical companies have enough incentive to produce quality goods due to their reputation. This idea is so mainstream in academic economics, that in 1994 while sitting in on a graduate Economics class at Emory University, taught by the chairman (Emory's term) of the department, the uselessness of the FDA was a foregone conclusion.
While I do see the value in "name brands", I think the practicality of reliance on "brand reputation" falls apart when you consider the huge amount of sub-contracting, mergers and acquisitions, short time horizons of corporations (one or two fiscal quarters), and bankruptcy that is prevalent in industry. On top of that, in a global economy, the value of reputation can be even more elusive.
See NPR story on global food supply:
Heinz makes this meal by combining more than 50 industrial food ingredients. Each ingredient has probably changed hands a dozen times on its way from the farm or the sea. Each one is sold and then resold to a chain of distributors, exporters, importers, and wholesalers before finally reaching Heinz. The 50 ingredients in this one tiny meal could easily have gone through 500 different suppliers, spread all over the globe.
Then, there is the question of equity. Poor people who buy cheap stuff from dollar stores won't be able to afford protection from bad food and medicine. How does abolishing the FDA solve that issue?
Also from Adam Davidson's NPR story linked to above:
As a rule, experts say, such suspicious products go to cut-rate restaurants and deep discount stores. They rarely go to established brand-name companies. And that means the food in any brand-name supermarket is very likely safe to eat — at least in the short run. Of course, shoppers still have to worry about all that sodium and fat.