I think it's important that there is a big difference between a farmer as in someone who is out in the field doing laborer, and a farmer as in a large landowner

I think it's important that there is a big difference between a farmer as in someone who is out in the field doing laborer, and a farmer as in a large landowner who has a lot of other people out in the fields doing labor which historically in China, and also Europe and the US, was considered to be a kind of ideal person in many time periods. So I doubt anyone who was out doing labor in the fields could do great in the exam, but if you were a small local elite, this provided a path for your children to potentially rise up.