No Pun Intended

Quite literally, I don't intend to put puns in this post. I do wish, though, to talk about intentionality. 

In writing, good things can happen without our intending them to (I do believe in inspiration), and good things are more likely to happen, perhaps, if we intentionally set out to make them happen (as in intentionally doing good research, intentionally proofreading, intentionally seeking feedback from others).  One intentionality I would advise against in college writing is the intentional fragment. 

To refresh your memory, a fragments are, as stated in the Purdue OWL, "incomplete sentences."   Often times they are written on accident, and sometimes a writer will write one on purpose (intentionally) for effect.  Examples of fragments include

You can stay at  my house.  Always.

Never having been there.

After reaching the conclusion that Andreas was one of the best filmmakers in Norway.

QUESTIONS:

Which of the three is most likely to be intentional?  Why?  How effective is its effect?  Why?

Why do you think I advise against intentional fragments in college writing?