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The point is that Python/bltinmodule.c/builtin_reduce()
masks the error returned from PyObject_GetIter(). Errors
from PyIter_Next() are not masked.

What about the following example:

class LazyFile:
   def __init__(self, name, mode="r"):
      self.name = name
      self.mode = mode
   def __iter__(self):
      return open(self.name, self.mode)
  
import operator
  
f = LazyFile("does not exist")
  
s = reduce(operator.add, f)

LazyFile *does* support iteration, but the underlying
problem of the non existing file is masked. Removing the
call PyErr_SetString(PyExc_TypeError, "reduce() arg 2 must
support iteration"); in builtin_reduce(), will produce the
original exception "IOError: [Errno 2] No such file or
directory: 'does not exist'" and when the second argument is
not iteratable, the original exception is just as good:

>>> reduce(lambda x,y: x+y, 42)
Traceback (most recent call last):
  File "<stdin>", line 1, in ?
TypeError: iteration over non-sequence