One thing I've noticed that many web designers don't realize is that there is a scholarly approach to creating web designs (and designing anything). There are elements of design and principles of design that apply whether you're building a web page or a paper brochure. But it can be argued that, like art, beautiful design is in the eye of the beholder, and someone who has never studied design principles could still create a good looking site. Do you think learning design principles is important to a web designer or should web designers be more flexible?


YES.
Sure “art is in the eye of the beholder”, but web sites, or at least business web sites are not art. The portion of “art sites” is relatively tiny.
If you learn the formal definitions you will know how and when you can “violate” them. Sure a few talented designers will be able to “intuitively” create good sites, but the majority will create drek or at least mundane sites.