Well, just think about it, people do all kinds of strange things to their bikes, from the pointless and possibly dangerous, to the moderately useful and mildly entertaining, to some rare examples of sheer biking genius.
So why haven't we seen anyone run double stems and bars?
Want a nice streamlined tuck available on your MTB? chuck in another stem, a set of drop bars and you're good to go.
Want a comfy upright climbing position and some serious brakes on your tourer? Another stem and a flat bar and you're suddenly fully compatible with everything the MTB world has to offer.
The guy who does the Shift mate also does some brake splitters and things like that I believe, so some functions would be possible to duplicate on both bars.
Now don't get me wrong, I'm not saying that this has to be a great idea. But it's so easily available, and it'd provide some really handy workarounds to troubles encountered while trying to set a bike up for use outside its intended envelope that I find it strange that I haven't seen it tried yet.