I once asked a question "Would RSA make sense if we used no computers?". The answer was negative, because finding primes that would make secure keys would prove too hard. Assuming that we had found another way of finding primes without computers, would RSA be usable in, for example, medieval times?
Many of the beginner explanations use very simple examples: like this
It is still hard to factorize a small number by hand, compared to other operations. There is definitely a size of prime numbers where hand computation is still feasible, but hand factorizing isn't. Would you, for instance, even armed with a list of primes, be able to quickly tell me what the prime decomposition of 1043 is?
It's 149 and 7. Slow to decompose, but easy to multiple by hand. You can go a lot bigger by hand or with an abacus etc.