Pokémon - No one has ever seen a Pokemon lay an egg

We all know Pokéggs appear out of thin air and high humidity.

This thing about the eggs has always baffled me. I mean, I get that kids are the games' target, but dammit, sometimes I think it can be pretty ridiculous. It's one of those things that push my suspension of disbelief far too much. How come nobody has ever seen a Pokémon laying an egg?

And don't bring me that "oh, the keepers say they don't know where it came from because they don't want to tell a kid that their Pokémon have been fucking non-stop since they left them", because this proves that nobody actually knows.

Seriously, Professor Elm has to be the worst Pokémon Professor in the universe, because not even him, supposedly an expert in breeding, knows how Pokémon reproduce.