I assume if it's vital infrastructure to a couple mega-farms they'll happily take over maintenance. They're not gonna just shut down operations because some rural bridges on their preferred routes aren't maintained anymore. They'll either accept longer routes using a smaller set of still-publicly-maintained bridges, or solve the problem some other way, maybe by maintaining the roads themselves. Public spending drops, and one or both of food prices go up slightly and profits go down slightly. Seems fine. May well be cheaper, overall—forcing companies to choose between longer routes and maintaining their own roads seems like a good way to weed out routes that are being maintained at a net loss.
Why do folks act like farmers are doing what they do out of altruism or something? "You owe farmers! They feed you!" Yeah, I do owe them. I owe them what I paid for the food. Right? If they decide I'm not sufficiently grateful they can stop. I'm not a "the market solves all problems" sort but I'm pretty sure it'd solve that one, no problem. Others will happily increase production to make up for the loss, because it's a market. Throw a fit that urbanites aren't subsidizing rural living & businesses enough, and stop producing, and someone with more sense will gladly take that market share.
If that wasn't the case, I am not sure the US would be a competitive position to grow staples compared with much of the rest of the world, which in itself is a whole topic of discussion.
Given that it already is being subsidized, I think thought needs to be done for handling the topic of broad agricultural good distribution and subsidies. Frankly I think corn, bioethanol, meat etc... should lose their subsidies but that in itself would be quite a vote loser.
E.G. How about canals, barges, railways instead of roadways
I just object to framing things like urbanites must subsidize rural living because "that's where their food comes from". Sure, of course... but that's why there's a food market. We're not propitiating the farm-gods to shower food upon us, but, instead, paying for food. Subsidies might make sense for several other reasons, but, as someone who spend much of his childhood in the country and sometimes living on small farms, the defensive "but you owe us" attitudes from some people when this topic comes up seem downright bizarre.
This would make subsidization more transparent to the general public, while also enabling free-market competition and innovation rather than free-money stagnation.
So you've got the rural 1/3rd of the population depending on 7x more roads and 20x more bridges than the urban population. If those folks actually bore the full cost of maintaining their own roads, I'd be willing to bet many of them would decide their rural lifestyle wasn't worth quite as much as they claimed.