Immutability and pure functions are not a panacea for programming. One of the very best explanations for allowing mutability comes from Péter Török in a StackOverflow answer:

Both mutable and immutable objects have their own uses, pros and cons.

Immutable objects do indeed make life simpler in many cases. They are especially applicable for value types, where objects don’t have an identity so they can be easily replaced. And they can make concurrent programming way safer and cleaner (most of the notoriously hard to find concurrency bugs are ultimately caused by mutable state shared between threads). However, for large and/or complex objects, creating a new copy of the object for every single change can be very costly and/or tedious. And for objects with a distinct identity, changing an existing object is much more simple and intuitive than creating a new, modified copy of it.

Think about a game character. In games, speed is top priority, so representing your game characters with mutable objects will most likely make your game run significantly faster than an alternative implementation where a new copy of the game character is spawned for every little change.

Moreover, our perception of the real world is inevitably based on mutable objects. When you fill up your car with fuel at the gas station, you perceive it as the same object all along (i.e. its identity is maintained while its state is changing) — not as if the old car with an empty tank got replaced with consecutive new car instances having their tank gradually more and more full. So whenever we are modeling some real-world domain in a program, it is usually more straightforward and easier to implement the domain model using mutable objects to represent real-world entities.

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