Apparently, the word empathy isn't as well understood as I thought.

Under typical usage, it refers to emotions, not full sensory input. Think Deanna Troi from star trek.

I've never actually heard/seen it used to refer to sensory input.

And, yes, even if it's "only" emotions that are picked up, it would be distracting. This would radically change human society. That's the entire point of the question in the post. It would be even more of a change with full sensory input though.

Imagine a world where that guy that's creeping along on the highway isn't just making people angry, because everyone that gets close knows that he's grieving so hard he can barely function. You feel that grief yourself. Or, if you prefer your interpretation of empathy, you can feel his bowels cramping and realize that he's going slow because he's looking for an exit.

Now, this doesn't automatically mean that everyone is going to act with kindness. But it does mean that none of us could ever again just dismiss someone else's state of being. We would know that the other person is a feeling being and that makes being cruel an entirely different proposition. Whe we would feel, just like it were our own pain, what our actions cause, it's gong to make people slow down and think before acting.