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.
You might think that Mario 64 was built with tickets and sprints, but, according to interviews, there was no master plan, only the principles that the game should feel good and be fun. They started with just Mario in a small room, and tuned his animations and physics until he felt nice and responsive. After that, the levels were also created as they went, with the designers, developers, and director going back and forth using sketches and prototypes.
Building like this is never a straight line. Ideas and code get left on the cutting room floor because part of innovation is questioning whether what you made should exist. The process is cyclical and iterative, looking something like this.