I guess that, as far as explanations on how encryption actually works, this analogy using paint and clocks is pretty good. My head more or less 'asploded when they got to the modulus math part, but I think I got the gist. The problem with nerds (and I most definitely have this problem) is they're so excited to tell you how something works they tend to neglect to tell you how to get it to work.
In other words, great, it's awesome how nifty public/private key encryption works. Now what's the easiest way to convey my plans for world domination to my worldwide network of minions in a way that will keep Smokey off my trail? And, wouldn't it have been easier for you to just say "use this!" and hand me a disk? Yes. Disks. There aren't any disks? Wait, when did 3.5" floppies go out of style?