The pure python version of lru_cache() wrappers supported weak references.  It's not essential, but I have used it a couple of times.  In the spirit of PEP 399, the C version should add back the weakref support (and a test).

I can submit a PR. Just making sure I understand, is this essentially the desired behavior change?

import weakref
import functools

if 0:
    from test.support import import_fresh_module
    functools = import_fresh_module('functools', blocked=['_functools'])

@functools.lru_cache
def f(x):
    return x

ref_to_f = weakref.ref(f)
print(ref_to_f)

# Current:
# TypeError: cannot create weak reference to 'functools._lru_cache_wrapper' object
# Desired:
# <weakref at 0x000001ABFE0F5090; to 'function' at 0x000001ABFE2D5AF0 (f)>

Yes.  That is the desired behavior.  Use Objects/setobject.c and Include/setobject.h as a model.

New changeset 1253c3ef70ea5632d32ae19579a14152db0d45c1 by Dennis Sweeney in branch 'master':
bpo-40504: Allow weakrefs to lru_cache objects (GH-19938)
https://github.com/python/cpython/commit/1253c3ef70ea5632d32ae19579a14152db0d45c1

Thanks for the PE :-)