Class definition of inner classes in __init__ of outer class

I would like to know if there is some downside or good reason not to define inner nested classes inside the __init__ of the outer class like shown below. I am considering this approach for my library API.

What I like about it is that the behavior of inner classes could be customized directly on subclasses of Outer and I have access to the Outer objects in each Inner class via self. Also I could define defaults on class level for each inner class but those defaults may be different for each instance of Outer.

class Outer:
    def __init__(self):
        class Inner1:
            param = 42  # default
            def __init__(inner, param=None):
                if param is not None:
                    inner.param = param

            def do_something(inner):
                print(inner.param)

        self.inner1 = Inner1


class OuterSub(Outer):
    def __init__(self):
        super().__init__()

        class Inner1(self.inner1):
            def do_something(inner):
                print(2*inner.param)
        self.inner1 = Inner1


outer = Outer()
outer_sub = OuterSub()

outer.inner1(2).do_something()
outer_sub.inner1.param = 5
outer_sub.inner1().do_something()