However, for some reason, unlike more common contractions, it is much more common in spoken English than in written.
There's definitely no rule against it. I wouldn't think anything of hearing "who're" everyday conversation. It's rare you see it in writing, though.
What you hear in every day speech is governed more by the mechanics of how your mouth works when you're speaking fluently, honestly. For example, if I were to say, "I would have done it" it most likely would come out sounding like "I'd've done it." Unless your intention was to get the sound across, though, you'd never, ever write that.
Yes, and perhaps more interestingly, what will it look like 500 years from now? Many common modern words that we assume to be self-contained turn out to be pastiches of two or more older words. Like "shire reeve" -> sheriff.
Well I'll be. That is so cool. Thanks!
http://www.etymonline.com/index.php?term=sheriff&allowed_in_...
Edit: Allow me to repay in kind. Did you know that rhubarb is called "rhubarb" because the Greeks thought only barbarians would eat it?
http://www.etymonline.com/index.php?term=rhubarb&allowed_in_...