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Anatoly,
msg107191 belongs to issue8903, not here and it is not a use case, but rather a demonstration of how the proposed feature would work.
My question is why would an application need current time without current date? I feel providing time.now() may lead so people to call date.today() and time.now() separately instead of datetime.now() leading to interesting bugs.
One think I would consider an improvement over the current situation, would be to rename date.today() to date.now(). There are too many ways to spell the same thing:
date.today()
datetime.today()
datetime.now().date()
and no easy way to write a "how long ago" function that would work for both date and datetime:
def ago(t):
 t.now() - t