> only exist to mutate state

Which part of the state, and when?

Is this your program?

   // change anything, anywhere, in the entire database, the biggest state
   execute_sql(user_input)

You might want controls around that state so not anyone can change it. It might be read only for some users - that is, immutable.

Is this your program?

    log_to_database(financial_event for $5.00)

You probably want your financial logs to be immutable. Nobody should be able to mutate that $5.00 event to be $500.00.

Is this your program?

    o.foo = complex_function(...)
    ... 1000 lines later ...
    o.foo = null
    ... 1000 lines later in another file ...
    o.foo.do_stuff() // oops! foo was set to null somehow - but where?
    

The above scenario has shared state with "foo". Somewhere it was set to null somewhere. It could be set to null anywhere in your program. Good luck tracking the bug. If "foo" was immutable, you would know immediately where null came from, because it can only be initialized one time. It lowers the cognitive load, knowing that certain actions are impossible makes it easier to focus on what matters.

Is this your program?

    thing = computation()
    return thing + 2

Many program are a series of computations - fresh state is created on each line, nothing is mutated. There is no reason not to be using immutability. In fact, if immutability were throughout, a compiler wouldn't have to worry about things like aliasing.

This is all the tip of the iceberg, there are many reasons to enjoy using immutability.

https://en.wikipedia.org/wiki/Aliasing_(computing)