Fundamentally, in the real world, the state associated with many particular identities will change. If I ask what is "the present position of Joe's Buick", today it might be a location in Seattle, and tomorrow it might be a location in Los Alamos. It would be possible to define and create a
GeographicLocation object whose value will always represent the location where Joe's Buick was at some particular moment in time and would never changes--if today it represents a spot in Seattle, then it will always do so. Such an object, however, would have no continuing identity as "the present location of Joe's Buick".
It may also be possible to define things so that there is a
VehicleLocation object which is connected to Joe's Buick such that the object always represents "the present location of Joe's Buick". Such an object could retains its identity as "the present location of Joe's Buick", even as the car moves around, but would not represent a constant geographical location. Defining "identity" may be tricky if one considers the scenario where Joe sells his Buick to Bob and buys a Ford--should the object track "the present location of Joe's Ford" or "the present location of Bob's Buick"--but in many cases such issues may be avoided by using a data model that guarantees that some aspects of object identity will never change.
It isn't possible for everything about an object to be immutable. If an object is immutable, then it cannot have an immutable identity that encapsulates anything beyond its current state. If an object is mutable, however, it can have an immutable identity whose meaning transcends its present state. In many situations, having an immutable identity is more useful than having an immutable state, and in such situations mutable objects are nearly essential. While it is possible in some cases to "simulate" mutable objects by having an immutable object which would search through the most recent version of an immutable objects to find information that may "change" between one version and the next, such an approaches are often extremely inefficient. Even if one could magically receive once per minute a bound book that gave the location of every vehicle everywhere, looking up "Joe's Buick" in the book would take a lot longer than merely asking a "present location of Joe's Buick" object which would always know where the car was.