The OpenWrapper function of io and _pyio is an undocumented hack allowing to use the builtin open() function as a method:

class MyClass:
    method = open

MyClass.method(...)    # class method
MyClass().method(...)  # instance method

It is only needed by the _pyio module: the pure Python implementation of the io module:
---

class DocDescriptor:
    """Helper for builtins.open.__doc__
    """
    def __get__(self, obj, typ=None):
        return (
            "open(file, mode='r', buffering=-1, encoding=None, "
                 "errors=None, newline=None, closefd=True)\n\n" +
            open.__doc__)

class OpenWrapper:
    """Wrapper for builtins.open

Trick so that open won't become a bound method when stored
as a class variable (as dbm.dumb does).

See initstdio() in [Python/pylifecycle.c](https://github.com/python/cpython/blob/main/Python/pylifecycle.c).
"""
__doc__ = DocDescriptor()

    def __new__(cls, *args, **kwargs):
        return open(*args, **kwargs)

The io module simply uses an alias to open:
---

OpenWrapper = _io.open # for compatibility with _pyio

No wrapper is needed since built-in functions can be used directly as methods. Example:
---

class MyClass:
    method = len  # built-in function

print(MyClass.method("abc"))
print(MyClass().method("abc"))

This example works as expected, it displays "3" two times.

I propose to simply remove io.OpenWrapper and force developers to explicitly use staticmethod:

class MyClass:
    method = staticmethod(open)

io.OpenWrapper is not documented.

I don't understand the remark about dbm.dumb: I fail to see where the built-in open() function is used as a method.

I also opened a discussion on python-dev about OpenWrapper and staticmethod:
https://mail.python.org/archives/list/python-dev@python.org/thread/QZ7SFW3IW3S2C5RMRJZOOUFSHHUINNME/

As for dbm.dumb, it was an attempt to make _Database._commit() working at the shutdown stage (it is indirectly called from __del__()). See bpo-723231. Although in Python 2 __builtin__.open != io.open, and in Python 3.0 the code already uses io.open directly.

I afraid that this code is not reliable (and never was reliable), because modules os and io can be cleared before calling it, so os.unlink and io.open would not work. But this is a different issue.

OpenWrapper was added in ce3a72a (bpo-1267) and was only used to set __builtin__.open (I suppose that at thet moment dumbdbm.py still set open as a class attribute).

It is still can be set as a class attribute in user code, so I think that removing OpenWrapper needs a deprecated period.

OpenWrapper was added in ce3a72a (bpo-1267) and was only used to set __builtin__.open

It is useless in CPython, since CPython always use the C implementation of the io module, and in the io module, io.OpenWrapper is just an alias to io.open.

$ python3
Python 3.9.2 (default, Feb 20 2021, 00:00:00) 
>>> import io
>>> io.OpenWrapper is io.open
True

(I suppose that at thet moment dumbdbm.py still set open as a class attribute).

I failed to find where in Lib/dbm/dumb.py the open() function is used to define a method. Maybe the code changed since OpenWrapper was added?

At commit ce3a72a, the io module was only implemented in Python (Lib/io.py, _io exist didn't exist). It was reimplemented in C in Python 3.1.

It is still can be set as a class attribute in user code, so I think that removing OpenWrapper needs a deprecated period.

I'm fine with deprecating the function by defining a __getattr__() function in io.py and _pyio.py. But only if it doesn't block the implementation of the PEP-597 ;-) The PEP-597 implementation issue is discussed at:
https://bugs.python.org/issue43510#msg389822

New changeset 77d668b by Victor Stinner in branch 'master':
bpo-43680: _pyio.open() becomes a static method (GH-25354)
77d668b

New changeset 3bc694d by Victor Stinner in branch 'master':
bpo-43680: Deprecate io.OpenWrapper (GH-25357)
3bc694d