You do want one site to look like another site. I know if is fun for designers to make up their own UI's, but there are well established patterns that work well, and that's what everyone should use. This is how everything was when people built desktop applications because you used the OS supplied widgets. These widgets were built be experts in HCI. Everything worked the same in every app, and nobody thought about it or wished they were all unique. CSS and the web are the worst things that ever happened to usability.
It's not just "fun," it's necessary to create an optimal user experience for every particular use-case. Have you ever played two video games which have the same UI? I'd be surprised if you have. Each and every one has its own interaction patterns, its own design language, and its own visual hierarchy.
I absolutely want the web to have better builtin widgets with common functionality and accessibility, but the point is not for them to look the same, but rather work the same.
