Without side-effects, you simply can't do certain things. One example is I/O, since making a message appear on the screen is, by definition, a side-effect. This is why it's a goal of functional programming to minimize side-effects, rather than eliminate them entirely.
Setting that aside, there are often instances where minimizing side-effects conflicts with other goals, like speed or memory efficiency. Other times, there's already a conceptual model of your problem that lines up well with the idea of mutating state, and fighting against that existing model can be wasted energy and effort.
