In your first example, you appear to assume that for calculations where "each mistake could cost $millions or lives", engineers who calculated by hand typically didn't double-check by redoing the calculation, so a second check with a 95% accuracy tool is better than nothing. This assumption is false. I suggest you watch the 2016 film Hidden Figures to understand the level of safety at NASA when calculations were done by hand. You are suggesting lowering safety standards, not increasing them.
Your third example is unclear. No calculators can perform factoring of large numbers, because that is the expected ability of future quantum computers that can break RSA encryption. It is also unclear why multiplication and division have different difficulties, when dividing by n is equal to multiplying by 1/n.
> It is also unclear why multiplication and division have different difficulties, when dividing by n is equal to multiplying by 1/n.
Well sure, but once you multiply by 1/n you leave N (or Z) and enter Q, and I suspect that's what makes it more difficult because Q is just a much more complex structure because it formally consists of equivalence relations. In fact it's easy to divide an integer x by an integer y, it's just x/y ... the problem is that we usually want the fraction in lowest terms, though.
>you appear to assume that for calculations where "each mistake could cost $millions or lives", engineers who calculated by hand typically didn't double-check by redoing the calculation
Not at all! For any n extra checks, having an n+1 phase that takes a 20th of the effort is beneficial. I did include triple-checks to gesture at this.
>It is also unclear why multiplication and division have different difficulties, when dividing by n is equal to multiplying by 1/n.
This actually fascinates me. Computers and human both take longer to divide than to multiply (in computers, by roughly an order of magnitude!) I'm not really sure why this is in a fundamental information theory kind of way, but it being true in humans is sufficient to make my point.
To address your specific criticism: you haven't factored out the division there, you've just changed the numerator to 1. I'd much rather do 34/17 in my head than 34 * (1/17).