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.
Back in 1969, Emil Ruder, a famous Swiss typographer, wrote on behalf of his contemporary print materials what we could easily say about our contemporary websites:
http://informationarchitects.jp/the-web-is-all-about-typography-period/