The premise of your argument is that "the outcome" can be separated from the process. This is true enough for manufacturing bricks: I don't much care what processes was used to create a brick if it has certain a compressive strength, mass, etc.
But Baumol's argument, which you introduced to the conversation, is that outcome and process cannot actually be distinguished, even if a distinction in thought is possible among economic theorists.
It's very true for healthcare (especially mental healthcare) and education today as well, because for most people, the choice isn't LLM vs. human attention - it's LLM vs. no access at all.
> But Baumol's argument, which you introduced to the conversation, is that outcome and process cannot actually be distinguished
How is that Baumol's argument? How is 'outcome' vs 'process' relevant to his argument at all?
'Cost disease' is just the foundational truth that the cost of the output from industries with stagnant productivity will increase due to the fact that the workers in that industry can be more valuable in other industries, reducing the number of relative workers in the stagnant industry.
If you want to make the output from a stagnant industry available to a broader spectrum of the population then you have to improve the productivity of that industry.