What would be the handling of a bike with reversed stem?
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.