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Posting an objective can channel the students inquiry and the activities especially if bound by time.  Total student-based inquiry can be all over the place ... so we as teachers need to direct it.

That being said, one school district I worked at made it mandatory to post objectives for each lesson and it had to list the PA Standards by number and phrase. So in this case, it was very high level, but the students did not care about it.  It sure looks good to the casual observer, but students had only a small idea about the inquiry process in learning the big idea.

I like to put up big ideas we are working on - usually on a side board or wall, and add to it as topics come up.  This keeps the students looking for these big ideas in the next few days of class.  I do not find it stiffling creativity or inquiry.