Simple solutions do exist... it's just, they're simple, so people solve them very quickly and nobody else even has time to start processing them as a "problem".
If people are still arguing about something ten years later, it's because it's not simple. But there's lots of stuff we don't argue about, because it's solved, because it was simple.
Simple solutions can be really hard to find sometimes (you know P != NP and all that). The thing you're talking about is solutions that are simple to think of.
If people are still arguing about something ten years later, it's because it's not simple. But there's lots of stuff we don't argue about, because it's solved, because it was simple.