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The idea of design patterns is to take a set of patterns and solve recurrent problems. At the same time (even in the same breath), the patterns reflect good object-oriented programming (OOP) practices. So, we cannot separate OOP from design patterns, nor would we want to do so.
In answering the question of why bother with design patterns, we are really dealing with the question of why bother with OOP. The standard response to both design patterns and OOP often points to working with a team of programmers and speaking the same language. Further, it's easier to deal with the complexities involved with programming tasks requiring a division of labor for a large project using an object metaphor and practices.