If last names are largerly based off previous occupation of our ancestors, why don't the vast majority of us have a last name that has to do with farming or agriculture in general if the majority of the population drew their livelhoods from agriculture?(I only know that this was the case in Europe, I do not know about other continents)
Occupational last names were useful if they were identifiers. John Smith referred to the only smith in the village. John Miller referred to the only Miller. John Farmer would be confusing, as most people were farmers.
Farmer is a last name in English, but it was probably given to people who were farmers in unusual places. That guy in the ship's crew who was always talking about cows and what crops to plant in which seasons, he might be called John Farmer.