IIRC, it's not that there's no tower farmer, it's that there's no capable tower farmer
I think they just don't care about it. All the other towers have tower farmers but dragons have no need for food so they look down on the job
I think it was because there's never been a farmer that's why they still doesn't understand what farmer does and they're curious on how job farmer is
a bit of spoiler:
---the dragons knew the job of tower farmer but its purpose was vague because each tower have different info about them
Spoiler warning
There is. It's a creature of the tower and I forgot if he left the tower or died.
Facts
So even the original tower masters didn't know about the Farmer job-class, that does mean that this job is a newly created class that was created by the tower system itself. My theory that it has a mind of its own is starting to become plausible.