Assigning __str__ method in __init__ not working as expected in Python [duplicate]

I tried to conditionally create the

__str__

method in a python class, as recommended here and here and I understand that is is not recommended to do this. But for my understanding, doing:

from types import MethodType

def str_fcn(self):
    return self.a

class A(object):
    def __init__(self, a=None):
        if a is not None:
            self.a = a
            self.__str__ = MethodType(str_fcn, self)
            self.test = MethodType(str_fcn, self)

a = A(a="name")

print(a)
print(a.test())

Does not seem to work for magic methods. The last print call at the end prints "name" as I expect, but the first uses the default string representation. Why?