Yes, it would definitely benefit society if we used more bicycles. First of all, there would be the obvious health benefit of riding bicycles more often for excessive. Additionally, there would be less traffic and congestion and there would be much less pollution and CO2 emissions. It would be a great idea for people living in the city.
Obesity, and fossil fuel consumption are two of the biggest problems plaguing society today. The use of bicycles more in transportation helps both of these problems, aiding people in getting exercise, and reducing the number of cars on the road, which will reduce our dependence of gasoline as well as reduce our consumption of fossil fuels.
I believe society would benefit more if bicycles were used more for transportation. I believe there would be more than one benefit. Bicycle use cuts back on emissions for cars, so this is a fairly large benefit on its own. Using a bicycle also improves the health of those using them. When this happens en masse, people are healthier on the whole.
The problem with using bicycles more is that the United States tends to spread out. Unlike European urban areas the US tends to spread out across large areas. This mean that either people would need to become fitter to bike to these locations or a lot more time to get from one place to the other. Because US citizens tend to either take the easiest method or need things immediately I doubt they would be willing to bicycle to locations rather than drive.
In cities and communities where there are bike lanes, more bicycle use is a good idea. In most areas though, bikes have to share the roads with cars, slowing automobiles down, clogging up traffic and causing accidents. This all adds up to the existing stresses of urban environments and drives up costs.