When I avoid multiplying large numbers in my head, that's because I can easily characterize the problem and reliably use a calculator.
Neither are the same as people trying to use LLMs to unreliably replacing critical thinking.
This differs from closed-form calculations where a calculator is normally constrained to operate--there is one correct answer. In other words "a random calculation mistake" would be undesirable in a domain of functions (same input yields same output), but would be acceptable and even desirable in a domain of uncertainty.
We are surprised and delighted that LLMs can produce code, but they are more akin to natural language outputs than code outputs--and we're disappointed when they create syntax errors, or worse, intention errors.
I don't follow this statement: if anything, we absolutely must check the resut of an LLM for the reason you mention. For coding, there are tools that attempt to check the generated code for each answer to at least guarantee the code runs (whether it's relevant, optimal, or bug-free is another issue, and one that is not so easy to check without context that can be significant at times).