Some functions can be described by the single signature. See examples in msg285647. Selected examples:

  dict.pop(key)
  dict.pop(key, default)

  type(obj)
  type(name, bases, mapping)

  range(stop)
  range(start, stop, step=1)

  min(iterable, *, key=identity)
  min(iterable, *, default, key=identity)
  min(*args, key=identity)

I think the only way to resolve this problem is to add the support of multiple signatures in inspect, pydoc, Argument Clinic, etc.

Signature object provides methods like .bind(), which will be hard to define if a function has many signatures.  Also, inspect.signature currently returns one Signature object, that shouldn't be changed.

Wouldn't it be easier instead of this:
  type(obj)
  type(name, bases, mapping)

do this:
  type(obj_or_name, bases=None, mapping=None)

And explain what really is going on in the docstring?

It can be do, but I don't think it is worth. Making bases and mapping optional arguments does not make much sense to me. And there is no a value that can be used as a default value for the second parameter in dict.pop().