Is the idea that the worldwide agricultural system would be gradually overtaxed and then collapse within a short period?

Things like that are not unprecedented. I think that is the theory for what became of the Easter Island civilization. One could also draw parallels to the collapse of sardine fishing in US in the 1950s -- in a couple of years the sardine population completely crashed, but up until that point the fishing had been going great, there was no gradual cost increase that made it less profitable.