My first job out of uni was in creating automated tests to validate some set top box. It involved using library of "blocks" to operate a remote control. Some of the people I have been working with spent their whole career in this narrow area, building those libraries of block and using them for customer and I have no doubts a LLM can today produce the same tests without any human intervention
Replacing labor doesn't require replacing whole jobs, it's enough to only replace specific tasks within those jobs which will reduce the number of workers needed for the same amount of work.
To pick a rather extreme example, the fraction of the population involved in farming is rather lower than in the past. Due to productivity improvements.
It's not clear why your analogy wouldn't have implied the end of white collar work when computers were first invented or when the internet was invented. Both of those should have been massive productivity boosts which meant the workers would have to go elsewhere to feed themselves. Instead Jevon's paradox kicks in every time.
I think it was the GPS, automation (robotics), bioengineered crops, and conglomerates. My point is, I'm pretty sure it's a lot of factors. Even in the cotton gin case. It's probably naïve to give so much credit to one thing
Most QA, most analyst positions, a good chunk of the kludge in intellectually challenging jobs, like medical diagnostics or software engineering, most administrative work, including in education and in healthcare, about 80% of customer success, about 80% of sales, are all within striking distance of automation with current-generation LLMs. And taht's entirely ignoring the 2nd-order effects in robotics and manufacturing.
You don't need LLM to replace QA. Just fire them, push some testing to developers and the rest to the users. Shareholders will be pleased by budget efficiency!
