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The problem with your example does not lie with zip(). 
Instead, there is a misunderstanding of iter() and how
iterators are consumed.  Instead of iter(), the correct
function is itertools.tee():
>>> zip(*tee([1,2,3,4]))
[(1, 1), (2, 2), (3, 3), (4, 4)]

Also, stylistically, the zip(*func) approach is too opaque.
 It is almost always better (at least for other readers and
possibly for yourself) to write something more obvious in
its intent and operation.  List comprehensions and generator
expressions are often more clear and easier to write correctly:
>>> [(x,x) for x in [1,2,3,4]]
[(1, 1), (2, 2), (3, 3), (4, 4)]

I do agree that the word sequence should be dropped because
it implies that non-sequence iterables are not acceptable as
arguments.  That's too bad because the word "sequence" seems
to help people understand what zip is doing.

You're correct that the zip docs do not describe its
implementation in such detail as to be able to predict the
[(1,2),(3,4)] result.  However, that would be an
over-specification.  That particular result is an
implementation specific detail that is subject to change. 
It probably won't change, but we don't want to encourage
people to write code that relies on the specific order of
operations within zip().  If someone wants to do something
tricky, such as [(1,2),(3,4)], then they are better off
writing an explicit loop so that the order of operation is
clear both to themselves and to code reviewers.