A milkman should should be able to deliver milk. A watchman should be able to watch. A developer should be able to develop. These ideas no longer apply for people that hope to be able to do a lot more.
These days it is extremely important that a developer be able to understand the different aspects of marketing and sales. That the accountant have a working knowledge of the products manufactured and sold in different markets. Knowledge of functioning of other departments helps people better appreciate their own jobs. It helps people develop human understanding of problems. More often than not this human and emotional understanding of problems helps people want to work harder towards actually solving problems rather than just fretting about problems that have presented themselves. It also allows for real team work.
So a web designer learning programming and learning what a web browser really is like might not seem to make much of a difference. But in the real world, it might just. Think about it for just a few minutes. If a web designer learns more about resource allocation and more about programming he will likely be able to predict the behaviour of the web browser, and that is simply not easy. But that will help the development effort cut down on wastage and cut down loading time maybe even improving interactivity.
It also helps you get promotions and allows you to give people your advice on everything.