95% of the information on the web is written language. It is only logical to say that a web designer should get good training in the main discipline of shaping written information, in other words: Typography.
Building structure requires serious listening, serious reflection, and serious imagination. All this requires experience, and no matter how experienced you are, it costs you. We spend our time and nerves to save users their time and nerves. Well-designed things give us the invaluable present of time. Well-designed products do not just save us time, they make us enjoy the time we spend with them. They make us feel that someone has been thinking about us, that a nice person took care of the little things for us. This is mainly why we perceive well-designed things as more beautiful the longer we use them, and the more used they become.
We didn't have Google in the early days. Other search engines like Lycos, Excite and Northern Lights did exist but were nowhere near as efficient as modern search engines. Finding something you were interested in was not as simple as typing a few words and getting to that information in one click.
No, the web was much more of an adventure. It was a place that you wandered to discover new areas, like exploring the vast open seas. A new virtual space that lead to all kinds of strange, interesting, exciting places. This is what the web was like, at least, in our collective imagination.
Google has become the de facto gatekeeper of the web, an arbiter of what is useful and what should get visibility. Except, most websites that appear on the first page, the links that you are most likely to click on—less than 1% of searchers click on something in the second page—are designed to be there by optimising for Google's algorithms. One consequence of this is that most of the websites that people get to "organically" are created by professionals and marketers who "position" themselves on those keywords. This means that the smaller, amateur web gets hidden in the shadows of web professionals who design around specific keywords and audiences.
It is worth remembering a website does not have to be a product; it can also be art. The web is also a creative and cultural space that need not confine itself to the conventions defined by commercial product design and marketing.