Like most things in a developers life, it depends. Even on the front end, especially in a browser context, understanding patterns is important. It helps to understand why certain behaviors happen and how to avoid bottlenecks. It also depends on the complexity of what you are working with. There's a reason why certain patterns become more popular than others.
Beyond this, I personally hate being pigeon-holed as a "front end developer." I understand database structures and why certain approaches are better in some situations vs others. I know how communication channels work, and why one might implement things in a certain way on the middle-tiers. I can work across the stack. Most "full-stack" developers are weak on the front end. And many "front-end" developers are weak all around. I think it's up to each individual to be the best they can be across as broad a field as is appropriate for them.
Even in the front end, it's important to understand how and why certain things work. Why you'd use an object as a dictionary, instead of a lookup on an array. The little things add up. When you understand many of the typical patterns, you see them take shape in what you touch, even if you aren't writing them.