> Farmers got rich because all of sudden their manual labour capacity was multiplied by machines.

This sounds like a semantic disagreement.

I think you are using the word "farmer" to mean "large agricultural landlord". Today, those terms may have a lot of overlap, because most of us don't work in agriculture like we did then, but in the past, it wasn't so much the case.

Back then, the landlord who had the "big house" wasn't called a farmer, but often a "Lord" or "Master".

"Farmers" were mostly people who worked as tenants on their land. The confusion in US history started early as the local feudal lords of the time (the founding fathers) rebranded themselves as farmers in opposition to their British rulers, but the economic structure of the societies was scarcely different.