I'm not convinced about trade secrets being the capitalistic route here, specially since, as pointed out somewhere else, the current system is basically like trade-secrets already, which suggest inverted causality.

In a pure free market, someone could try to keep the formulas secret, but others can just reverse engineer it into being public, which is basically guaranteed to happen if there's sufficient demand. Given that they aren't wasting money trying to obfuscate the recipe nor the formula, these competitors do have an advantage over the original. As such, I posit that free-to-copy will be default behavior in a pure free market, with trade-scerets being resteicted on niche sectors.

The reason we can't do this today is primarily that reverse engineering is heavily restricted by IP laws.