I think people feel that once the pool of humans required to do a thing diminishes to the point that their occupation is rare enough to be invisible, that is essentially the same as "fully automating" it.
I have certainly never met anyone who works in "loom engineering" in my entire life.
Randomly, I spent an afternoon with a team of loom engineers long ago. In 1989, I took a month-long trip to the USSR. Trips for Americans back then were guided / chaperoned by the Soviet government, with the clear intention of showing off what the Soviet system was capable of. To see their manufacturing prowess, we spent an entire afternoon touring an automated bed-sheet factory and talking with the team that designed and maintained the machines. I don't remember much other than the intense noise and the large number of machines with white cotton sheets coming out.
All the sheets we saw in that factory, and in our hotels, were noticeably thicker and stiffer than American sheets, somewhere between American sheets and denim. When we asked about that, they seemed to feel sorry that we only had thin, flimsy sheets.
Are they a rare artisan rather than a commodity? Maybe a subtype or cross-trained variation of some other wider job role?