What makes the 18-200 so bad for landscapes compared to, say, the 17-55?
Well, the 18-200 is what's known as a super-zoom. Its impressive, because it allows you to zoom the lens 10x from 18-200, while the 17-55 only does 3x, but, to do that they have to make sacrifices in the lens design. For example, the 18-200 has a lot of distortion on the wide end (from 18-25ish), and isn't very sharp on the tele end (from 150-200ish). The 17-55 on the other hand has less distortion, and is generally reviewed as being much sharper. The distortion might not bug you, but the sharpness can show up on canvas prints.
But, if you do a lot of landscapes, I'd say go for even wider than 17mm.
I had no idea that the difference between 18mm and 10/11mm was that big. In that case, wouldn't upgrading to the 24-105 here be a bad idea compared to the 18mm I have now?
Yeah, the difference between 10mm and 24mm is doubling the field of view. While the subject of this photo isn't good, it should give you some perspective on how big the difference is. In an outdoor scene, the difference is even bigger. And for a lens like the 10-22, you can still shoot in the 18-22 range, but you have the ability to go much, much wider when you need to to include everything.