Sorry, modifying these mature APIs is a really bad idea.  They are worked well as-is of over a decade.  Seeing people use None for these arguments makes the code less readable. 

Python has a number of APIs where the number of arguments controls the behavior.  For example, type() with one argument does something very different that type() with three arguments.  Likewise, iter() behaves differently with two arguments than three.  The pattern used by index() shows-up in a number of places where we have optional start and end arguments.  These APIs are a long standing Python norm, both for the core and for third-party modules.  Type checking will have to adapt to norms rather than having all of Python change for the convenience of typing.

Serhiy, please go ahead with the doc fix.

If the OP really wants to insist on changing old and stable APIs through out the language in a way that I consider harmful to readability, we can battle it out in a PEP and on mailing lists.