I think you are a bit ignorant of how people act.
There is a reason the USDA and FDA exist. Look into history, and see what was being passed off as food before they came into being.
A “Free Market” doesn’t really exist. For one thing, the meat packers would start adding a lot more extenders (non meat products), and stop the inspection process. And they would have no reason to tell you or anyone about it.
Actually, I'm taking into account how people act. With strict regulation comes strict methods of how to game the system, and that's exactly what people do.
To take a more practical example, look at mutual funds today. People will invest in them, not knowing at all what they are investing in, or how it is managed, simply because they trust regulators to keep everything on the up and up. And year after year, more and more people are having every penny of their savings stolen because they are trusting the regulations, and ignoring any form of common sense.
If you put a lottery machine right next to a slot machine, and ask people which has a more likely chance of giving a payoff, people will point to the state lottery time and time again - it's more regulated, it's run by the state, it of course must have better odds. If you ask them which has a higher 'rake' or taking for the house - the overhead of the game, they'll again say that the lottery is better. It's state run, they wouldn't rip us off.
Tons of accidents happen each year because people trust a stop sign to actually stop traffic, or walk out into the street because a walk sign says it's ok to go, without even looking to see that oncoming car which was running the yellow.
When you assure people that someone else is looking after their risk, any common sense goes out the window. And that's why, after sixty years of ever increasing regulation and strict guidelines, the end results of food borne illness is still the same - a one in six chance of it happening to any American each and every year.