What is the purpose of python's inner classes?

Is there something that can't be accomplished without them?

No. They are absolutely equivalent to defining the class normally at top level, and then copying a reference to it into the outer class.

I don't think there's any special reason nested classes are ‘allowed’, other than it makes no particular sense to explicitly ‘disallow’ them either.

If you're looking for a class that exists within the lifecycle of the outer/owner object, and always has a reference to an instance of the outer class — inner classes as Java does it – then Python's nested classes are not that thing. But you can hack up something like that thing:

import weakref, new

class innerclass(object):
    """Descriptor for making inner classes.

    Adds a property 'owner' to the inner class, pointing to the outer
    owner instance.
    """

    # Use a weakref dict to memoise previous results so that
    # instance.Inner() always returns the same inner classobj.
    #
    def __init__(self, inner):
        self.inner= inner
        self.instances= weakref.WeakKeyDictionary()

    # Not thread-safe - consider adding a lock.
    #
    def __get__(self, instance, _):
        if instance is None:
            return self.inner
        if instance not in self.instances:
            self.instances[instance]= new.classobj(
                self.inner.__name__, (self.inner,), {'owner': instance}
            )
        return self.instances[instance]


# Using an inner class
#
class Outer(object):
    @innerclass
    class Inner(object):
        def __repr__(self):
            return '<%s.%s inner object of %r>' % (
                self.owner.__class__.__name__,
                self.__class__.__name__,
                self.owner
            )

>>> o1= Outer()
>>> o2= Outer()
>>> i1= o1.Inner()
>>> i1
<Outer.Inner inner object of <__main__.Outer object at 0x7fb2cd62de90>>
>>