Well, you ride on the road because it is safer.
Forester in "Effective Cycling" found that cyclists had much lower accident rates on the road then on bike paths or sidewalks. Interestingly enough, the cyclists with the lowest accident rates were cyclists who commuted to work and who therefore rode in heavy traffic.
Interestingly enough, cycling on the road is less hazardous then being in a motorized vehicle on the road (about 1/2 as dangerous). I know it doesn't feel that way. But I thought about it. Most motorists kill themselves by driving under the influence, falling asleep at the wheel or driving way too fast for conditions. It is hard to ride a bike when you are plastered and I don't think many people even try. Most cyclists are awake when they ride. And it is pretty hard to ride fast enough on a bike to put your life in danger with excessive speed (except for monster downhills of course).
I recall, doing a multiday tour on the roads from Lansing MI to Saint Ignace - about 400 miles. At the end of the tour, we did a 7 mile ride around Macinaw Island which has no cars and lots of bike paths. At the end of that ride, my nerves were shot. I had far more near misses from dern fools on bikes on the narrow paths then I had in 4 days on the roads. The interesting thing was the horses on the trails were far more predictable then the idiot humans! I swore that I was going to stick to the roads with the semis where it is safe! Our only accident on the tour happened on Macinaw Island. A kid on a bike T boned one of our riders on an intersection - the kid had built up a pile of speed on a downhill. Our guy was not hurt - just a bit of road rash and bruises but his bike frame was bent.