I'm not sure how the conclusion follows from the premises. Farm subsidies do consume federal funds. Where do you think the funding for the massive pork-barrel farm bills comes from? Moreover, those dollars aren't necessarily passed on to consumers. In theory, the market for farm products is a perfectly competitive market and any subsidy to the market would result in cheaper prices for everyone. In practice, well, Cargill exists. Large agribusinesses are quite capable of taking subsidy rents and stashing them away as profit rather than using them to compete on prices if their market is more like a cartel and less like a perfectly competitive free market.

What does this have to do with a subsidy? You can do this identically without a subsidy (assuming you can do it at all). The subsidy just lowers the starting price.