What can `init` do that `new` cannot?

Question

Note about difference between new and init

Before explaining missing functionality let’s get back to definition of __new__ and __init__:

__new__ is the first step of instance creation. It’s called first, and is responsible for returning a new instance of your class.

However, __init__ doesn’t return anything; it’s only responsible for
initializing the instance after it’s been created.

Consequences of replacing init with new

Mainly you would lose out on flexibility. You would get a lot of semantics headaches and loose separation of initializatin and construction (by joining __new__ andinit we are to joining construction and initialization into one step…).
Let’s take a look on snippet below:

class A(object):
    some_property = 'some_value'

    def __new__(cls, *args, **kwargs):
        obj = object.__new__(cls, *args, **kwargs)
        obj.some_property = cls.some_property
        return obj


class B(A):
    some_property = 2

    def __new__(cls, *args, **kwargs):
        obj = super(B, cls).__new__(cls)
        return obj

Consequences of moving __init__ actions into __new__:

Initialize B before A: When you are using __new__ method instead of __init__ your first step of creating new instance of B is calling A.__new__ as side effect you cannot initialize B before A is initialized ( access and assign some properties to new B instance). Using of __init__ gives you such flexability.
Loose control on initializing order: let’s imagine that you have B_N inherited from two classes (A_N1, A_N2), now you would miss controlling of order of initializing new instance of B_N(what is the order you are going to initialize instances ? it could be matter… what is weird.)
Properties and methods mess: you would miss access to A.some_property (cls would be equal to B while instantiating new instance of B. However directly accessing of A.some_property is possible, but my guess it’s at least weird to access properties within class throught class name and not by using classmethods).
You cannot re-initialize an existed instance without creating new one or implementation special logic for this ( thanks to @platinhom for idea )