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.
On ChrisHallquist's post extolling the virtues of money, the top comment is Eliezer pointing out the lack of concrete examples. Can anyone think of any? This is not just hypothetical: if I think your suggestion is good, I will try it (and report back on how it went)
I care about health, improving personal skills (particularly: programming, writing, people skills), gaining respect (particularly at work), and entertainment (these days: primarily books and computer games). If you think I should care about something else, feel free to suggest it.
I am early-twenties programmer living in San Francisco. In the interest of getting advice useful to more than one person, I'll omit further personal details.
Budget: $50/day
If your idea requires significant ongoing time commitment, that is a major negative.