Who here can read Japanese?

But words are spoken without any kanji, and people seem to understand each other just fine.

Also, that sentence looks nightmare-ish.

Words are spoken in context though. However, I do know what you're getting at. It's the same reason you can say "I saw a knight at night" and people would get it. However, it doesn't work when written. If "knight" were spelled the same as "night" it looks stupid. "I saw a night at night."

What? See how it gets confusing that way? Doesn't help that there are a crapload of kanji that share pronunciation, unlike English where most words try to not sound like each other.

Sure, it's fine when spoken, but it's confusing when written. I remember a really nice English example somewhere that I read in high school or something for English class. It was a really long story that overused the word "wood", "would", etc. I think it did, from what I remember. I wouldn't call it a tongue twister, but it was pretty horrible to read through.