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Argument Clinic currently prevents the "impl" function from ever seeing the "args" tuple or the "kwargs" dict. There should be a way to ask it to pass those values in to the "impl" function.

So, let's think about this for a minute. What's the API that we *want* here?
If your function has the signature
 (a, b, c=20, *args)
and you call it with
 (1, 2, 3, 4, 5)
should "args" be (4, 5), or (1, 2, 3, 4, 5)?
I assert that the impl function should get the same "args" (and "kwargs") that a Python function would--that is, post-argument-processing. In the above example "args" should get (4, 5).
This might be somewhat painful to do in round 1, where we're still leveraging off PyArg_ParseTuple*. But in the future it'll be cheaper to do it this way. In any case, it's the right API, so that's what we should do.
(Adding Nick just to see if he agrees--he had a use case for *args in the builtin module.)

Yes, I agree we should follow the Python level semantics, and only capture the excess positional arguments. For the record, the four builtins I flagged as needing this in order to add introspection information:
__build_class__
- 2 positional only args, arbitrary additional args
- checks size with PyTuple_GET_SIZE
- uses PyTuple_GET_ITEM x2 + PyTuple_GetSlice to unpack
print
- only arbitrary position args, iterates and extracts using PyTuple_GetItem
- uses PyArg_ParseTupleAndKeywords with an empty tuple to extract the keyword-only args
min
max
- use a shared helper function min_max
- uses the args tuple directly if size > 1
- otherwise uses PyArg_UnpackTuple to extract the supplied iterable
- uses PyArg_ParseTupleAndKeywords with an empty tuple to extract the keyword-only args
- this "one arg means iterable" style API might need to be a special case...

I think at first step we can support var-positional parameter only when there are no other positional parameters, and var-keyword parameter only when there are no other keyword parameters. So print, max and dict.update will be supported, but __build_class__, map and functools.partial are not.

I'll try to implement the support of var-positional parameters.

In case it is helpful, here's my list of examples where the AC and existing signature objects are insufficiently expressive:
type(obj)
type(name, bases, mapping)
 two different signatures depending on type 
range(stop)
range(start, stop)
range(start, stop, step)
dict.pop(key[, default])
 default of None has different meaning than missing default
 which raises KeyError when the key is missing
itertools.permutations(iterable[, r])
 where the absence of *r* implies r=len(iterable)
bisect.bisect_right(a, x[, lo[, hi]]) -> index
 where the absence of *hi* implies hi=len(a)
min(iterable, *[, default=obj, key=func]) -> value
min(arg1, arg2, *args, *[, key=func]) -> value
 has two signatures depending on the number of
 positional arguments and a keyword argument
 only used in the first signature. It's implementation
 is also shared with max().
dict() -> new empty dictionary
dict(mapping) -> new dictionary initialized from a mapping object's
 (key, value) pairs
dict(iterable) -> new dictionary initialized as if via:
 d = {}
 for k, v in iterable:
 d[k] = v
dict(**kwargs) -> new dictionary initialized with the name=value pairs
 in the keyword argument list. For example: dict(one=1, two=2)
def sumseq(seq, a=0, b=None):
 # Pure python code with nullable int
 if b is None:
 b = len(seq)
 return sum(seq[a:b])

FYI I started to work on a different Argument Clinic enhancement, issue #29299: "Argument Clinic: Fix signature of optional positional-only arguments".

Thank you for your examples Raymond, but they don't directly related to this issue, implementing support of var-positional and var-keyword parameters. I believe that it is possible to solve it, and the solution is complex, but is not extremal hard. I'm working on the first part of this.
Your examples show other, more hard issue. It looks to me that the only solution of that issue is to add support of multiple signatures for functions. But this can break the API of the inspect module.

Once this feature will be implemented, print() should be modified to use Argument Clinic: see the issue #29296.

New changeset f88e138a1aa3b9a9e013963e4fd7d5cce6a0b85c by Ken Jin in branch 'main':
bpo-20291: Fix MSVC warnings in getargs.c (GH-27211)
https://github.com/python/cpython/commit/f88e138a1aa3b9a9e013963e4fd7d5cce6a0b85c