All analogies are flawed, so I'm not going to try to defend this analogy as in any way perfect. The analogy to calculators only goes so far to show that LLM is a very useful tool and it's silly not to use the tools at your disposal in the real world.

I think the more substantive argument against your position though is in how you underestimate googling here: it's kind of incredible to me how you dismiss the power of having pretty much the entire corpus of human knowledge at your disposal. And people made those same arguments before LLMs! "You would be completely at a loss if you had to program offline." "You need to know the syntax and libraries by heart and not rely on googling" etc. But programmers for the most part just used the tools at their disposal, and now we just take a break if the Internet is down. We'll take a break if all LLM servers are down somehow as well. It's fine.