It's really just one of a class of similar idioms: Who would have guessed! Who would have dreamed! Who would have known! Who knew? Notice that I used exclamation points. They are 'rhetorical' questions, i.e. a question that is being posed without any real expectation of an answer. There's no need to go beyond the ending verb, because the implied answer for all of them is 'no one'. You can use the question mark if you wish. I suppose it depends on how amazed the speaker is. You will also hear them in a contracted form: Who'd have thought? Who'd have known? ...etc.

Who would have thought. (full stop) - yup commonly use. Who would have thought (about) it. (full stop) - just add the about.

Who would have thought. In general, if something is shorter, people will say it. Alexander gets shortened to Alex, unless the person specifies that you call them by their full name all the time.