I don't think this argument is very convincing. For example, why limit the application of this rationale to food supply? Why trust the market (i.e., corporations) with _anything_. Is our government strictly superior to the market in all cases, or does the market have some strengths that the government lacks? If so, why are those strengths the wrong tradeoff for this case in particular but perhaps not for others? Without more nuance, this argument could support socialism (as in "the government completely owns production", not the capitalism-friendly democratic socialism).
Another issue is that we're not talking about complete ownership of the food supply, but only temporary ownership (i.e., patents have a lifetime) over individual food products that are individually subject to competition and regulation.
> While Monsanto owns the patents, they can legally wreck anyone who attempts to violate them. If the government owns the patents, "violation" doesn't exist because anyone can use them freely.
Patent enforcement is a feature, not a bug. We want people to invest in making food production more sustainable, so we need incentives. Notably, patents _do_ expire, so Monsato's (or whomever) risk is rewarded and society benefits. If the enforcement is too strict or the patents too long, we can adjust those knobs accordingly. No need smash the system because the knobs aren't tuned properly.