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.
Domain specific UX means understanding how the supply should fit the demand considering a specific situation and use case.
On the other hand, many aspects of UX don’t require knowledge about a particular situation. They‘re based on the common constraints of human sense faculties, memory and cognition or the net of ergonomic factors around the device and the setting where it’s used. These domain independent elements of the UX are important too.
Domain independent UX should absolutely pervade the organization. It belongs to the general skill and knowledge of each supplier at their link in the chain. It’s part of learning to be a good designer, programmer, marketer, salesperson etc.