A website is constantly changing and growing. Producing an excellent design to accommodate this is mostly impossible. Most large sites basically look the same and somewhat boring. Most small sites that try to be creatively designed are either designed poorly or have serious functional issues.
If you want quality design, it needs to be a work in progress. It's inspiring to see good design on paper: a movie poster, a menu, or an advertisement. It's good design because it's been crafted to fit its medium. On the web, the medium keeps changing as people switch devices and resize their windows. Designing to accommodate all media is more important than designing for design.
There are whole lot of us pushing web design forward. We're trying our best to work on all devices and have that sense of wonder that fixed media design can have. We make progress, but it's just going to take time.