No, no one cares about the final numbers - they are just, as the Bitcoin paper explains, Proof of Work. The only point of doing those calculations is to prove that you have spent X processor cycles in service of Bitcoin. You could entirely replace the calculation (and checkers) with a different calculation and nothing whatsoever would change about bitcoin, because no one cares about the values.

Conversely, if you found an algorithm that could compute those same values in microseconds on a calculator, bitcoin would plummet in an instant, because suddenly anyone with a calculator could run 99% attacks on the bitcoin network. The numbers aren't improtant, the busywork is.