Well, there's a lot to this issue and the article, while probably accurate in its own way, is only the tip of the iceberg. Different animals have had different antibiotics introduced into their feed for different reasons. As animals live in closer and closer quarters, i.e. dirtier and dirtier germ-labs, they've needed antibiotics to keep them from getting sick. That's one issue. Cows and hormones are another issue. And so on. But it's safe to say that in all cases, the "need" for more and faster and cheaper food is what has driven this, and that the outcome of antibiotics is now pretty clear, even if not 100% conclusive.
The article asks "how much more would we be willing to pay to not have antibiotics?" and the answer is already here- just look at farmers' markets and CSA's for the answer. Those of us who care pay "a lot" more because we realize that food prices are artificially low, and that if you factor in all the medical issues, government subsidies and so on that goes into the "cheaper" food, it's actually not so cheap. So bypassing that whole system and eating something raised better costs more in the short term and is cheaper in the long term.
As for farmers, they don't actually like using antibiotics because they cost money. But they don't really have a choice at this point- they're too invested in current farming infrastructure to just stop using antibiotics. It would mean an entire shift to a different kind of farming and they're just not going to do that after doing it the same way for 50 years. Hopefully, their kids who are not married to such ideas are more open to trying things differently.