You mean what kind of idiot driver wouldn't check the sidewalks, right? Sarcasm aside, you get places a lot faster if you're part of traffic and don't have to wait until all the cars are past to go through an intersection.

Also by riding on the sidewalk you're being kind of a huge dick to pedestrians.

I don't think it's simply an issue of the cyclist looking, though that is probably a large part. I've been nearly hit by drivers who clearly weren't paying attention when I was being very careful. In particular, drivers breaking the law can easily catch you off guard. The worst near-hit I've had was from a driver who ran a red light, and my brother was hit riding a bike while he was coming off the sidewalk into the crosswalk from a driver who ran a stop sign. Also, cars are much faster than bikes, so you could easily be surprised by a car that seemingly comes from nowhere.

With that being said, I do think that you can ride on the sidewalk in a way that minimizes your risk. Being careful near intersections would do that. However, given that the accident rate on straight segments of road is pretty low (not really higher than that riding on the sidewalk, as I recall, though I should verify), you can probably get more benefit by riding where you are most visible (in the road) and being careful. Doing other things to improve your visibility like using flashing lights or flourescent yellow helps too.

There's also the issue of being a dick to pedestrians by riding on the sidewalk, as mentioned by kalium.