Flipping the phase on one side will likely sound weird and unnaturally wide and more importantly inconsistent. If it ever plays back in mono the reverb will go away completely. Except in headphones (or earbuds more likely) nobody ever actually sits in the sweet spot to listen to your music. As you move away from the speakers, the image collapses to mono (and that reverb starts to disappear) and that's not the only way your nice stereo sound might end up playing back mono.