Some time ago I tried to come up with something that worked with pen and pencil, even if it used backup tables or something, to make a board game that would explain the concept to kids.

I wasn't very successful, and eventually gave up. It's hard to come with something simple that's easy to do in one direction, but moderately hard to do in the opposite across some skill levels.

Which, eventually makes the concept unintuitive, when explained through the lens or “simple, primary school math” (which is all most grown ups can deal with, without immediately reaching out for a phone/calculator).

So, the intuitive explanation that does work (for RSA) is the “I send you an open safe only I have the key for, you fill it, and you close it and send it to me.” That's instantly intuitive, and works. The rest… meh.