But then it becomes a competitive advantage for another firm to use the same employees to do more work, leading to the jobs not being replaced.

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.

Counterexample, not analogy.

To pick a rather extreme example, the cotton gin...

Well the question here if LLMs are the cotton gin or if they’re the combine/tractor thing that killed all the farming jobs.

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