I know the usual reasons that apply to general immutable classes, viz
There are mutable, thread safe wrappers as well for some types.
AtomicBoolean
AtomicInteger
AtomicIntegerArray
AtomicLong
AtomicLongArray
AtomicReference - can wrap a String.
AtomicReferenceArray
Plus some exotic wrappers
AtomicMarkableReference - A reference and boolean
AtomicStampedReference - A reference and int