It's worth noting that every time there's been estimations on carrying capacity applied to humans, it's eventually turned out to be wrong.
The reality is that we are not very efficient at agriculture in all of the places where agriculture is practiced. Most carrying capacity models make the assumption that we are at or near peak agricultural output, but this simply isn't true, so the models' predictive powers fall apart.
For an example from another industry, where people have been similarly predicting capacity-related doom since the 80s, look at oil. In the 80s, people thought we were going to run out of oil, because "proven accessible reserves" were dwindling. Between the innovations of low-cost fracking and more effective "proving" tools, this problem evaporated.
The moral of the story is that, where demand is high, capitalistic pressures means that, given enough time, we will always finds a way to open up more supply.
All this to say, be very critical of the assumptions made by whatever models you find, or doomsday claims you may come across. If agriculturalists are not concerned about this, the burden of evidence for us to be concerned should be rather high.
Exactly if Americans spent more resources on food there would be more innovative approaches in this sector. Currently food is too cheap and there is barely any opportunity for innovation.
Sorry, I'd rephrase my original statement a little bit for clarity. I didn't mean at all to say that "nowhere is efficient", which in retrospect is one valid way of interpreting my original statement.
It's not that agriculture isn't hyper-efficient in certain locales. It's that it could be more efficient, if its operators cared to invest in making it so. Until demand rises relative to supply (from supply shortages), there isn't a price pressure to innovate on efficiency. This doesn't stop the "big farms" from innovating, because "big farm crops" are a race-to-the-bottom commodity business. That's why we get more corn, soy beans, whatever every year.
This is all without mentioning the places where agriculture is rather undeveloped, compared to the places you mention (many locales in Africa, central Asia, even the United States and Canada).
