What would be the handling of a bike with reversed stem? There are short and long stems:


  What effect does changing the stem length have on my bikes handling


There are flat bars and there are curved back bars for comfort upright position:


There even seem to exist bikes with no stem (apparently called "with forward geometry"):




But I have never, ever seen a bike with stem, going back from the headtube towards the rider. Such a setup would provide extremely wide wheelbase, which seems to be a good idea in some scenarios. Why is this geometry never used?
I actually have a VO Grand Cru stem angled back toward me. With the trekking bars, it works for my modest mostly-upright-posture purposes. No effect on bike handling that I can tell. If I get a yen to lean further forward someday (unlikely, with my middle-aged back) I'll flip it.

Adjustable stems can also be persuaded to do this. So it's possible, just not common.